Relevant bibliographies by topics / Boolean Functional Synthesis

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Boolean Functional Synthesis'

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Published: 6 September 2023

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Journal articles on the topic "Boolean Functional Synthesis"

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Pashukov, Artem. "Application of Weight-Based Sum Codes at the Synthesis of Circuits for Built-in Control by Boolean Complement Method." Automation on transport 8, no. 1 (March 15, 2022): 101–14. http://dx.doi.org/10.20295/2412-9186-2022-8-1-101-114.

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This work considers the application of Boolean complement method for the organization of self-checking circuits of built-in control for the devices synthesized on being Field-Programmable Gate Arrays. Review is given for the application of Boolean complement method while using various noise-resistant codes. The example is demonstrated for control circuit synthesis with Boolean complement method. Algorithm for control system synthesis by Boolean complement method with the use of weight-based sum codes by module M is formulated. As an example, weighted codes are considered with the summation of weight categories by module M = 3 and M = 4 for these purposes. The given codes have only two control categories that simplifies their application for task solution on the design of functional diagnostics system by Boolean complement method. The comparative analysis of both codes with their use in the systems with Boolean complement has been pursued. The application of Boolean complement method on the basis of weight-based sum codes for synthesis of discrete devices has been suggested.
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Efanov, Dmitriy, and Tat'yana Pogodina. "Self-Dual Functional Gates for the Synthesis of Controllable Digital Systems." Transport automation research 9, no. 2 (June 13, 2023): 205–21. http://dx.doi.org/10.20295/2412-9186-2023-9-02-205-221.

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All self-dual analogs of elementary functional gates have been considered, the use of which allows for the synthesis of self-dual circuit implementations of arbitrary Boolean functions. In this case, two synthesis methods can be used, each one based on the property of any Boolean function to be transformed into a self-dual function using one additional variable. The first method involves replacing all non-self-dual functional gates in the device structure with self-dual analogs. The second one involves obtaining a self-dual function from the original formula. The study conducted modeling of self-dual functional gates in pulse mode of operation. It has been shown that all self-dual functional gates, except for those implementing equivalence and nonequivalence functions (modulo-2 addition), are fully self-checkable with respect to stuck-at faults when checking computations based on the belonging of the generated functions to the class of self-dual Boolean functions. However, the gates that implement the mentioned functions require additional monitoring. For them, error masking occurs due to the simultaneous distortion of signals on both combinations in a pair. This feature of these self-dual functional gates should be taken into account when developing controllable self-checking digital computing devices and systems. The article provides an example of using methods for constructing self-dual circuit implementations. The obtained results can be used in the synthesis of controllable self-dual computing devices and systems.
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Rawski, Mariusz. "Application of Indexed Partition Calculus in Logic Synthesis of Boolean Functions for FPGAs." International Journal of Electronics and Telecommunications 57, no. 2 (June 1, 2011): 209–16. http://dx.doi.org/10.2478/v10177-011-0029-4.

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Application of Indexed Partition Calculus in Logic Synthesis of Boolean Functions for FPGAsFunctional decomposition of Boolean functions specified by cubes proved to be very efficient. Most popular decom-position methods are based on blanket calculus. However computation complexity of blanket manipulations strongly depends on number of function's variables, which prevents them from being used for large functions of many input and output variables. In this paper a new concept of indexed partition is proposed and basic operations on indexed partitions are defined. Application of this concept to logic synthesis based on functional decomposition is also discussed. The experimental results show that algorithms based on new concept are able to deliver good quality solutions even for large functions and does it many times faster than the algorithms based on blanket calculus.
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Abdollahi, Afshin, Mehdi Saeedi, and Massoud Pedram. "Reversible logic synthesis by quantum rotation gates." Quantum Information and Computation 13, no. 9&10 (September 2013): 771–92. http://dx.doi.org/10.26421/qic13.9-10-3.

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A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a recursive functional bi-decomposition approach is proposed to automatically synthesize a given function. While Boolean reversible logic is particularly addressed, our framework constructs intermediate quantum states that may be in superposition, hence we combine techniques from reversible Boolean logic and quantum computation. {The proposed approach results in quadratic gate count for multiple-control Toffoli gates without ancillae, linear depth for quantum carry-ripple adder, and $O(n\log^2 n)$ size for quantum multiplexer.
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BRAHA, DAN. "Design-as-satisfiability: A new approach to automated synthesis." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 15, no. 5 (November 2001): 385–99. http://dx.doi.org/10.1017/s0890060401155022.

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This article addresses computational synthesis systems that attempt to find a structural description that matches a set of initial functional requirements and design constraints with a finite sequence of production rules. It has been previously shown by the author that it is computationally difficult to identify a sequence of production rules that can lead to a satisficing design solution. As a result, computational synthesis, particularly with large volumes of selection information, requires effective design search procedures. Many computational synthesis systems utilize transformational search strategies. However, such search strategies are inefficient due to the combinatorial nature of the problem. In this article, the problem is approached using a completely different paradigm. The new approach encodes a design search problem as a Boolean (propositional) satisfiability problem, such that from every satisfying Boolean-valued truth assignment to the corresponding Boolean expression we efficiently can derive a solution to the original synthesis problem (along with its finite sequence of production rules). A major advantage of the proposed approach is the possibility of utilizing recently developed powerful randomized search algorithms for solving Boolean satisfiability problems, which considerably outperform the most widely used satisfiability algorithms. The new design-as-satisfiability technique provides a flexible framework for stating a variety of design constraints, and also represents properly the theory behind modern constraint-based design systems.
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Prihozhy, Anatoly A. "Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (December 14, 2021): 84–97. http://dx.doi.org/10.33581/2520-6508-2021-3-84-97.

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The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the method consists in extending the Shannon and Davio expansions of a Boolean function on a single variable to the expansions of the same Boolean function on another function with obtaining decomposition products that are represented by incompletely defined Boolean functions. Uncertainty in the decomposition products gives remarkable opportunities for minimising the graph representation of the specified function. Instead of two outgoing branches of the binary diagram vertex, three outgoing branches of the if-diagram vertex are generated, which increase the level of parallelism in reversible and quantum circuits. For each transformation step, appropriate mapping rules are proposed that reduce the number of lines, gates and the depth of the reversible and quantum circuit. The comparison of new results with the results given by the known method of mapping the vertices of binary decision diagram into cascades of reversible and quantum gates shows a significant improvement in the quality of quantum circuits that are synthesised by the proposed method.
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Perkowski, Marek A., Malgorzata Chrzanowska-Jeske, Andisheh Sarabi, and Ingo Schäfer. "Multi-Level Logic Synthesis Based on Kronecker Decision Diagrams and Boolean Ternary Decision Diagrams for Incompletely Specified Functions." VLSI Design 3, no. 3-4 (January 1, 1995): 301–13. http://dx.doi.org/10.1155/1995/24594.

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This paper introduces several new families of decision diagrams for multi-output Boolean functions. The introduced families include several diagrams known from literature (BDDs, FDDs) as subsets. Due to this property, these diagrams can provide a more compact representation of functions than either of the two decision diagrams. Kronecker Decision Diagrams (KDDs) with negated edges are based on three orthogonal expansions (Shannon, Positive Davio, Negative Davio) and are created here for incompletely specified Boolean functions as well. An improved efficient algorithm for the construction of KDD is presented and applied in a mapping program to ATMEL 6000 fine-grain FPGAs. Four other new families of functional decision diagrams are also presented: Pseudo KDDs, Free KDDs, Boolean Ternary DDs, and Boolean Kronecker Ternary DDs. The last two families introduce nodes with three edges and require AND, OR and EXOR gates for circuit realization. There are two variants of each of the last two families: canonical and non-canonical. While the canonical diagrams can be used as efficient general-purpose Boolean function representations, the non-canonical variants are also applicable to incompletely specified functions and create don't cares in the process of the creation of the diagram.. They lead to even more compact circuits in logic synthesis and technology mapping.
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Stojkovic, Suzana, Milena Stankovic, and Claudio Moraga. "Complexity reduction of Toffoli networks based on FDD." Facta universitatis - series: Electronics and Energetics 28, no. 2 (2015): 251–62. http://dx.doi.org/10.2298/fuee1502251s.

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Synthesis of switching functions by Toffoli gates has become a very important research topic in the last years, since Toffoli gates are used in the synthesis of reversible circuits. Early methods based on the truth-table representation of Boolean functions are applicable to functions with a relatively small number of variables. Later on, methods for synthesis by Toffoli gates based on decision diagrams (BDDs, FDDs or OKFDDs) were introduced and applied to the synthesis of both reversible and irreversible functions. This paper presents a method for the reduction of the number of lines and gates in the Toffoli gate realization of Boolean functions based on their Functional Decision Diagram (FDD) representation. Experiments show that, when the proposed reduction is used, the realization of the given function based on FDD will, on the average, be smaller in terms of the number of lines and the number of gates than the realizations based on an OKFDD, an optimal BDD or based on a FDD by using previously defined algorithms.
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Efanov, D. V., and D. V. Pivovarov. "FUNCTIONAL APPROACH TO THE SYNTHESIS OF CONCURRENT ERROR-DETECTION CIRCUIT BASED ON BOOLEAN COMPLEMENT AND USE OF "2-OUT-OF-5" CONSTANT-WEIGHT CODE." Informatika i sistemy upravleniya, no. 4 (2021): 81–94. http://dx.doi.org/10.22250/isu.2021.70.81-94.

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A method for self-checking concurrent error-detection circuit synthesis based on Boolean com-plement and "2-out-of-5" constant-weight code is described. The method is notable for using functional relationship between the signals from the working and control outputs instead of ana-lyzing the unit performance on each input. The functional dependence is established with due account to the requirements for the formation of codewords of the "2-out-of-5" code and a com-plete tester check. In addition, it considers the formation of a complete set of test combinations for transformation elements in the concurrent error-detection circuit. A method for obtaining a functional relationship between the control outputs and the operating outputs of the diagnostic object is presented. One of the options for extending the definition of the control function values is presented, as well as the functional dependence. It is noted that the number of options for ex-tending the definition of the control function values is large, which allows numerous options for synthesizing a concurrent error-detection circuit for any diagnostic object based on the described method. The use of the "2-out-of-5" code for the synthesis of concurrent error-detection circuits applying the Boolean complement method proved its effectiveness for organizing self-checking digital devices in automatics and computer technology.
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SELVARAJ, HENRY, PIOTR SAPIECHA, MARIUSZ RAWSKI, and TADEUSZ ŁUBA. "FUNCTIONAL DECOMPOSITION — THE VALUE AND IMPLICATION FOR BOTH NEURAL NETWORKS AND DIGITAL DESIGNING." International Journal of Computational Intelligence and Applications 06, no. 01 (March 2006): 123–38. http://dx.doi.org/10.1142/s1469026806001782.

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General functional decomposition is mainly perceived as a logic synthesis method for implementing Boolean functions into FPGA-based architectures. However it also has important applications in many other fields of modern engineering and science. In this paper, advantages of functional decomposition are demonstrated on "real life" examples. Application of decomposition-based methods in other fields of modern engineering is presented. In the case of decision tables, application of decomposition methods leads to significant benefits in the analysis process of data dependencies, especially in cases when the input decision tables are unmanageably large. Experimental results demonstrate that it can help implementing sequential machines using flip-flops or ROM memory. It also can be efficiently used as multilevel logic synthesis method for VLSI technology.
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Dissertations / Theses on the topic "Boolean Functional Synthesis"

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Martins, Mayler Gama Alvarenga. "Funtional composition and applications." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/164440.

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Este trabalho apresenta a composição funcional (CF) como um novo paradigma para realização da síntese lógica de blocos combinacionais. CF usa uma abordagem ascendente para sintetizar funções Booleanas, sendo capaz de avaliar os custos das funções intermediárias e explorando dessa forma um grande número de combinações diferentes de funções candidatas. Há vantagens interessantes quando comparado à abordagem descendente da decomposição funcional. CF apresenta grande flexibilidade para criar algoritmos com resultados ótimos ou subótimos para diferentes aplicações. A estratégia proposta apresenta bons resultados para síntese de funções Booleanas visando diferentes tecnologias. CF é baseado nos seguintes princípios: (1) representação de funções lógicas como um par ligado com representações funcional e estrutural; (2) o algoritmo começa de um conjunto de funções iniciais; (3) funções mais simples são associadas para criar funções mais complexas; (4) existe uma ordem parcial que permite o uso da programação dinâmica; (5) um conjunto de funções permitidas pode ser mantido para reduzir o tempo de execução/consumo de memória. Este trabalho apresenta algoritmos de composição funcional para fatoração Booleana, incluindo fatoração ótima, fatoração considerando o operador OU-exclusivo, computação de cadeias mínimas de decisão e síntese de funções considerando somente portas lógicas majoritárias e inversores.
This work presents functional composition (FC) as a new paradigm for combinational logic synthesis. FC is a bottom-up approach to synthesize Boolean functions, being able to evaluate the cost of intermediate sub-functions, exploring a larger number of different candidate combinations. These are interesting advantages when compared to the top-down behavior of functional decomposition. FC presents great flexibility to implement algorithms with optimal or suboptimal results for different applications. The proposed strategy presents good results for the synthesis of Boolean functions targeting different technologies. FC is based on the following principles: (1) the representation of logic functions is done by a bonded pair of functional and structural representations; (2) the algorithm starts from a set of initial functions; (3) simpler functions are associated to create more complex ones; (4) there is a partial order, enabling dynamic programming; (5) a set of allowed functions can be used in order to reduce execution time/memory consumption. This work presents functional composition algorithms for Boolean factoring, including optimal factoring, Boolean factoring considering the exclusive-OR operator, minimum decision chain computation and synthesis of functions considering only majority and inverter logic gates.
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Martinelli, Andres. "Advances in Functional Decomposition: Theory and Applications." Doctoral thesis, SICS, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21180.

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Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research.
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Martinelli, Andrés. "Advances in Functional Decomposition: Theory and Applications." Doctoral thesis, KTH, Mikroelektronik och Informationsteknik, IMIT, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4135.

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Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research.
QC 20100909
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Callegaro, Vinicius. "Read-polarity-once functions." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/87583.

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Algoritmos exatos para fatoração estão limitados a funções Booleanas read-once, onde cada variável aparece uma vez na equação final. No entanto, estes algoritmos apresentam duas restrições principais: (1) eles não consideram funções Booleanas incompletamente especificadas, e (2) eles não são adequados para as funções binate. Para superar o primeiro inconveniente, é proposto um algoritmo que encontra equações read-once para funções Booleanas incompletamente especificadas, sempre que possível, é proposto. Com respeito à segunda limitação, é apresentada uma transformação de domínio que divide variáveis binate existentes em duas variáveis unate independentes. Tal transformação de domínio conduz a funções Booleanas incompletamente especificadas, que podem ser eficientemente fatoradas mediante a aplicação do algoritmo proposto. A combinação das duas contribuições dá resultados ótimos para uma nova classe de funções Booleanas chamada read-polarity-once, onde cada polaridade (positiva ou negativa) de uma variável aparece no máximo uma vez na forma fatorada da expressão Booleana. Resultados experimentais sobre circuitos ISCAS'85 mostrou que funções read-polarity-once são significativamente mais frequentes em circuitos reais quando comparado com a classe de funções read-once, a qual muitos trabalhos já foram dedicados na literatura.
Efficient exact factoring algorithms are limited to read-once functions, in which each variable appears once in the final Boolean equation. However, those algorithms present two main constraints: (1) they do not consider incompletely specified Boolean functions; and (2) they are not suitable for binate functions. To overcome the first drawback, it is proposed an algorithm that finds read-once formulas for incompletely specified Boolean functions, whenever possible. With respect to the second limitation, a domain transformation that splits existing binate variables into two independent unate variables is presented. Such domain transformation leads to incompletely specified Boolean functions, which can be efficiently factored by applying the proposed algorithm. The combination of both contributions gives optimal results for a novel broader class of Boolean functions named as read-polarity-once functions, where each polarity (positive or negative) of a variable appears at most once in the factored form. Experimental results over ISCAS'85 benchmark circuits have shown that read-polarityonce functions are significantly more frequent than read-once functions, for which many works have already been devoted in the literature.
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Dubrova, Elena Vladimirovna. "Boolean and multiple-valued functions in combinational logic synthesis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ34259.pdf.

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Peh, Lawrence T. W. "An efficient algorithm for extracting Boolean functions from linear threshold gates, and a synthetic decompositional approach to extracting Boolean functions from feedforward neural networks with arbitrary transfer functions." University of Western Australia. Dept. of Computer Science, 2000. http://theses.library.uwa.edu.au/adt-WU2003.0013.

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[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Artificial neural networks are universal function approximators that represent functions subsymbolically by weights, thresholds and network topology. Naturally, the representation remains the same regardless of the problem domain. Suppose a network is applied to a symbolic domain. It is difficult for a human to dynamically construct the symbolic function from the neural representation. It is also difficult to retrain networks on perturbed training vectors, to resume training with different training sets, to form a new neuron by combining trained neurons, and to reason with trained neurons. Even the original training set does not provide a symbolic representation of the function implemented by the trained network because the set may be incomplete or inconsistent, and the training phase may terminate with residual errors. The symbolic information in the network would be more useful if it is available in the language of the problem domain. Algorithms that translate the subsymbolic neural representation to a symbolic representation are called extraction algorithms. I argue that extraction algorithms that operate on single-output, layered feedforward networks are sufficient to analyse the class of multiple-output networks with arbitrary connections, including recurrent networks. The translucency dimensions of the ADT taxonomy for feedforward networks classifies extraction approaches as pedagogical, eclectic, or decompositional. Pedagogical and eclectic approaches typically use a symbolic learning algorithm that takes the network’s input-output behaviour as its raw data. Both approaches construct a set of input patterns and observe the network’s output for each pattern. Eclectic and pedagogical approaches construct the input patterns respectively with and without reference to the network’s internal information. These approaches are suitable for approximating the network’s function using a probably-approximately-correct (PAC) or similar framework, but they are unsuitable for constructing the network’s complete function. Decompositional approaches use internal information from a network more directly to produce the network’s function in symbolic form. Decompositional algorithms have two components. The first component is a core extraction algorithm that operates on a single neuron that is assumed to implement a symbolic function. The second component provides the superstructure for the first. It consists of a decomposition rule for producing such neurons and a recomposition rule for symbolically aggregating the extracted functions into the symbolic function of the network. This thesis makes contributions to both components for Boolean extraction. I introduce a relatively efficient core algorithm called WSX based on a novel Boolean form called BvF. The algorithm has a worst case complexity of O(2 to power of n divided by the square root of n) for a neuron with n inputs, but in all cases, its complexity can also be expressed as O(l) with an O(n) precalculation phase, where l is the length of the extracted expression in terms of the number of symbols it contains. I extend WSX for approximate extraction (AWSX) by introducing an interval about the neuron’s threshold. Assuming that the input patterns far from the threshold are more symbolically significant to the neuron than those near the threshold, ASWX ignores the neuron’s mappings for the symbolically input patterns, remapping them as convenient for efficiency. In experiments, this dramatically decreased extraction time while retaining most of the neuron’s mappings for the training set. Synthetic decomposition is this thesis’ contribution to the second component of decompositional extraction. Classical decomposition decomposes the network into its constituent neurons. By extracting symbolic functions from these neurons, classical decomposition assumes that the neurons implement symbolic functions, or that approximating the subsymbolic computation in the neurons with symbolic computation does not significantly affect the network’s symbolic function. I show experimentally that this assumption does not always hold. Instead of decomposing a network into its constituent neurons, synthetic decomposition uses constraints in the network that have the same functional form as neurons that implement Boolean functions; these neurons are called synthetic neurons. I present a starting point for constructing synthetic decompositional algorithms, and proceed to construct two such algorithms, each with a different strategy for decomposition and recomposition. One of the algorithms, ACX, works for networks with arbitrary monotonic transfer functions, so long as an inverse exists for the functions. It also has an elegant geometric interpretation that leads to meaningful approximations. I also show that ACX can be extended to layered networks with any number of layers.
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Fiszer, Robert Adrian. "Synthesis of Irreversible Incompletely Specified Multi-Output Functions to Reversible EOSOPS Circuits with PSE Gates." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/2109.

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As quantum computers edge closer to viability, it becomes necessary to create logic synthesis and minimization algorithms that take into account the particular aspects of quantum computers that differentiate them from classical computers. Since quantum computers can be functionally described as reversible computers with superposition and entanglement, both advances in reversible synthesis and increased utilization of superposition and entanglement in quantum algorithms will increase the power of quantum computing. One necessary component of any practical quantum computer is the computation of irreversible functions. However, very little work has been done on algorithms that synthesize and minimize irreversible functions into a reversible form. In this thesis, we present and implement a pair of algorithms that extend the best published solution to these problems by taking advantage of Product-Sum EXOR (PSE) gates, the reversible generalization of inhibition gates, which we have introduced in previous work [1,2]. We show that these gates, combined with our novel synthesis algorithms, result in much lower quantum costs over a wide variety of functions as compared to our competitors, especially on incompletely specified functions. Furthermore, this solution has applications for milti-valued and multi-output functions.
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Kothamachu, Varun Bhaskar. "An investigation into dynamic and functional properties of prokaryotic signalling networks." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/26597.

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In this thesis, I investigate dynamic and computational properties of prokaryotic signalling architectures commonly known as the Two Component Signalling networks and phosphorelays. The aim of this study is to understand the information processing capabilities of different prokaryotic signalling architectures by examining the dynamics they exhibit. I present original investigations into the dynamics of different phosphorelay architectures and identify network architectures that include a commonly found four step phosphorelay architecture with a capacity for tuning its steady state output to implement different signal-response behaviours viz. sigmoidal and hyperbolic response. Biologically, this tuning can be implemented through physiological processes like regulating total protein concentrations (e.g. via transcriptional regulation or feedback), altering reaction rate constants through binding of auxiliary proteins on relay components, or by regulating bi-functional activity in relays which are mediated by bifunctional histidine kinases. This study explores the importance of different biochemical arrangements of signalling networks and their corresponding response dynamics. Following investigations into the significance of various biochemical reactions and topological variants of a four step relay architecture, I explore the effects of having different types of proteins in signalling networks. I show how multi-domain proteins in a phosphorelay architecture with multiple phosphotransfer steps occurring on the same protein can exhibit multistability through a combination of double negative and positive feedback loops. I derive a minimal multistable (core) architecture and show how component sharing amongst networks containing this multistable core can implement computational logic (like AND, OR and ADDER functions) that allows cells to integrate multiple inputs and compute an appropriate response. I examine the genomic distribution of single and multi domain kinases and annotate their partner response regulator proteins across prokaryotic genomes to find the biological significance of dynamics that these networks embed and the processes they regulate in a cell. I extract data from a prokaryotic two component protein database and take a sequence based functional annotation approach to identify the process, function and localisation of different response regulators as signalling partners in these networks. In summary, work presented in this thesis explores the dynamic and computational properties of different prokaryotic signalling networks and uses them to draw an insight into the biological significance of multidomain sensor kinases in living cells. The thesis concludes with a discussion on how this understanding of the dynamic and computational properties of prokaryotic signalling networks can be used to design synthetic circuits involving different proteins comprising two component and phosphorelay architectures.
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Besson, Thierry. "Optimisation de ROBBDs et applications." Grenoble INPG, 1996. http://www.theses.fr/1996INPG0190.

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La synthese logique est a l'origine de l'evolution des systemes numeriques et de l'informatique. De nombreux problemes peuvent se ramener a une serie d'operations sur des fonctions booleennes aussi bien en electronique numerique, en intelligence artificielle, recherche operationnelle que dans le domaine du test ou de la preuve formelle. Depuis que ce domaine est etudie plusieurs representations de fonctions booleennes ont ete introduites: table de verite, representation en somme de monomes, somme exclusive de produits et les diagrammes de decision binaire ou bdds. Le grand interet des bdds est que ceux-ci offrent une representation canonique des fonctions booleennes extremement compact. Malheureusement, le point faible de cette representation reside dans le fait que sa taille est etroitement liee a l'ordre des variables. Cette these consistera donc a trouver des methodes d'ordonnancement des variables d'un bdd de facon a ce que celui-ci soit de taille minimisee. Une application interessante de ces resultats peut-etre faite pour resoudre les problemes de decomposition technologique sur des composants a base de multiplexeurs et notamment sur les cellules actels du nom de la meme compagnie
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Dubrova, Elena Vladimirovna. "Boolean and multiple-valued functions in combinational logic synthesis." Thesis, 1997. http://hdl.handle.net/1828/8276.

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The subject of this dissertation is the theory of Boolean and multiple-valued functions. The main areas considered are: functional completeness, canonical forms, minimization of functions, discrete differences and functional decomposability. The results obtained are used as a foundation for the development of several new algorithms for logic synthesis of combinational logic circuits. These include an efficient algorithm for three-level AND-OR-XOR minimization for Boolean functions, an algorithm for generating the composition trees for Boolean and multiple-valued functions in a certain class, and an algorithm for computing a new canonical form of multiple-valued functions. Several other problems, related to logic synthesis, such as test generation for combinational logic circuits and synthesis of easily testable circuits are also addressed. Possible directions for future research are discussed.
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Books on the topic "Boolean Functional Synthesis"

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Porwik, Piotr. Widmowe modelowanie systemów cyfrowych o zadanych cechach. Katowice: Wydawn. Uniwersytetu Śląskiego, 2000.

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Kim, Jinwon. A cube-based recursive goal-oriented method for the synthesis of Boolean logic functions. Ottawa: National Library of Canada = Bibliothèque nationale du Canada, 1993.

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Sokolov, Artem, and Oleg Zhdanov. Cryptographic constructions on the basis of functions of multivalued logic. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1045434.

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Symmetric encryption algorithms have been successfully used to protect information during transmission on an open channel. The classical approach to the synthesis of modern cryptographic algorithms and cryptographic primitives on which they are based, is the use of mathematical apparatus of Boolean functions. The authors demonstrate that the use to solve this problem of functions of multivalued logic (FML) allows to largely improve the durability of the cryptographic algorithms and to extend the used algebraic structures. On the other hand, the study of functions of multivalued logic in cryptography leads to a better understanding of the principles of cryptographic primitives and the emergence of new methods of describing cryptographic constructions. In the monograph the results of theoretical and experimental studies of the properties of the FML, the presented algorithms for generating high-quality S-blocks for the symmetric encryption algorithms, as well as full-working samples of the cryptographic algorithms ready for practical implementation. For students and teachers and all those interested in issues of information security.
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Book chapters on the topic "Boolean Functional Synthesis"

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Akshay, S., Supratik Chakraborty, and Sahil Jain. "Counterexample Guided Knowledge Compilation for Boolean Functional Synthesis." In Computer Aided Verification, 367–89. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37706-8_19.

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AbstractGiven a specification as a Boolean relation between inputs and outputs, Boolean functional synthesis generates a function, called a Skolem function, for each output in terms of the inputs such that the specification is satisfied. In general, there may be many possibilities for Skolem functions satisfying the same specification, and criteria to pick one or the other may vary from specification to specification.In this paper, we develop a technique to represent the space of Skolem functions in a criteria-agnostic form that makes it possible to subsequently extract Skolem functions for different criteria. Our focus is on identifying such a form and on developing a compilation algorithm for this form. Our approach is based on a novel counter-example guided strategy for existentially quantifying a subset of variables from a specification in negation normal form. We implement this technique and compare our performance with those of other knowledge compilation approaches for Boolean functional synthesis, and show promising results.
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Lin, Yi, Lucas M. Tabajara, and Moshe Y. Vardi. "ZDD Boolean Synthesis." In Tools and Algorithms for the Construction and Analysis of Systems, 64–83. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99524-9_4.

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AbstractMotivated by applications in boolean-circuit design, boolean synthesis is the process of synthesizing a boolean function with multiple outputs, given a relation between its inputs and outputs. Previous work has attempted to solve boolean functional synthesis by converting a specification formula into a Binary Decision Diagram (BDD) and quantifying existentially the output variables. We make use of the fact that the specification is usually given in the form of a Conjunctive Normal Form (CNF) formula, and we can perform resolution on a symbolic representation of a CNF formula in the form of a Zero-suppressed Binary Decision Diagram (ZDD). We adapt the realizability test to the context of CNF and ZDD, and show that the Cross operation defined in earlier work can be used for witness construction. Experiments show that our approach is complementary to BDD-based Boolean synthesis.
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Fried, Dror, Lucas M. Tabajara, and Moshe Y. Vardi. "BDD-Based Boolean Functional Synthesis." In Computer Aided Verification, 402–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41540-6_22.

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Akshay, S., Supratik Chakraborty, Ajith K. John, and Shetal Shah. "Towards Parallel Boolean Functional Synthesis." In Tools and Algorithms for the Construction and Analysis of Systems, 337–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-54577-5_19.

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Scholl, Christoph. "Realizations of Boolean Functions." In Functional Decomposition with Applications to FPGA Synthesis, 1–22. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3393-8_1.

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Akshay, S., Supratik Chakraborty, Shubham Goel, Sumith Kulal, and Shetal Shah. "What’s Hard About Boolean Functional Synthesis?" In Computer Aided Verification, 251–69. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96145-3_14.

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Chakraborty, Supratik. "Boolean Functional Synthesis: From Under the Hood of Solvers." In Logic and Its Applications, 11–22. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-26689-8_2.

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Gittis, Andreas, Eric Vin, and Daniel J. Fremont. "Randomized Synthesis for Diversity and Cost Constraints with Control Improvisation." In Computer Aided Verification, 526–46. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13188-2_26.

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AbstractIn many synthesis problems, it can be essential to generate implementations which not only satisfy functional constraints but are also randomized to improve variety, robustness, or unpredictability. The recently-proposed framework of control improvisation (CI) provides techniques for the correct-by-construction synthesis of randomized systems subject to hard and soft constraints. However, prior work on CI has focused on qualitative specifications, whereas in robotic planning and other areas we often have quantitative quality metrics which can be traded against each other. For example, a designer of a patrolling security robot might want to know by how much the average patrol time needs to be increased in order to ensure that a particular aspect of the robot’s route is sufficiently diverse and hence unpredictable. In this paper, we enable this type of application by generalizing the CI problem to support quantitative soft constraints which bound the expected value of a given cost function, and randomness constraints which enforce diversity of the generated traces with respect to a given label function. We establish the basic theory of labelled quantitative CI problems, and develop efficient algorithms for solving them when the specifications are encoded by finite automata. We also provide an approximate improvisation algorithm based on constraint solving for any specifications encodable as Boolean formulas. We demonstrate the utility of our problem formulation and algorithms with experiments applying them to generate diverse near-optimal plans for robotic planning problems.
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Yarlagadda, R. K. Rao, and John E. Hershey. "Boolean Functions." In Hadamard Matrix Analysis and Synthesis, 51. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6313-6_14.

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Ferraz, Evandro C., Jeferson de Lima Muniz, Alexandre C. R. da Silva, and Gerhard W. Dueck. "Synthesis of Majority Expressions Through Primitive Function Manipulation." In Advanced Boolean Techniques, 135–58. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20323-8_6.

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Conference papers on the topic "Boolean Functional Synthesis"

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Tabajara, Lucas M., and Moshe Y. Vardi. "Factored boolean functional synthesis." In 2017 Formal Methods in Computer-Aided Design (FMCAD). IEEE, 2017. http://dx.doi.org/10.23919/fmcad.2017.8102250.

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Akshay, S., Jatin Arora, Supratik Chakraborty, S. Krishna, Divya Raghunathan, and Shetal Shah. "Knowledge Compilation for Boolean Functional Synthesis." In 2019 Formal Methods in Computer Aided Design (FMCAD). IEEE, 2019. http://dx.doi.org/10.23919/fmcad.2019.8894266.

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Rawski, Mariusz, and Piotr Szotkowski. "Reversible logic synthesis of boolean functions using functional decomposition." In 2015 MIXDES - 22nd International Conference "Mixed Design of Integrated Circuits & Systems". IEEE, 2015. http://dx.doi.org/10.1109/mixdes.2015.7208547.

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Golia, Priyanka, Friedrich Slivovsky, Subhajit Roy, and Kuldeep S. Meel. "Engineering an Efficient Boolean Functional Synthesis Engine." In 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD). IEEE, 2021. http://dx.doi.org/10.1109/iccad51958.2021.9643583.

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Rawski, Mariusz, and Piotr Szotkowski. "Reversible synthesis of incompletely specified Boolean functions using functional decomposition." In Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, edited by Ryszard S. Romaniuk and Maciej Linczuk. SPIE, 2017. http://dx.doi.org/10.1117/12.2281040.

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Morawiecki, Pawel, Mariusz Rawski, and Henry Selvaraj. "Application of Functional Decomposition in Synthesis of Boolean Function Sets." In 2008 19th International Conference on Systems Engineering (ICSENG). IEEE, 2008. http://dx.doi.org/10.1109/icseng.2008.65.

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Zhukov, Vladimir Vladimirovich. "Synthesis method and complexity bounds for programms with some structural restrictions." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-11.

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The work is devoted to the study of various classes of software circuits. type that implement Boolean functions, and the establishment of asymptotic estimates of Shannon functions for the complexity of implementing Boolean functions in schema classes. Models are introduced and explored reflexive-recursive schemes of functional elements and programs, in which recursive procedure calls are allowed. Influence is being explored the depth of recursion on the complexity of the implementation of the functions of the algebra of logic. For considered models, methods for the synthesis of schemes and programs are proposed, implementing arbitrary Boolean functions, as well as getting methods lower bounds for the Shannon function for the complexity of implementing Boolean functions, with the help of which, under certain restrictions, it was the asymptotic behavior of the corresponding Shannon functions is established.
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Shafat, Gabriel, Binyamin Abramov, and Ilya Levin. "Using Threshold Functions in Teaching Electronics." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59125.

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Teaching of digital electronics and the teaching of analog electronics differ significantly. The methods in use today differ in two major points: the required mathematical background and the used didactic methods. The well-known gap between the analog and the digital paradigms in teaching electronics has motivated the present study. The paper introduces a novel approach for electronics course teaching. The approach uses a concept threshold functions. Threshold functions have three remarkable properties that are suitable for the purposes of teaching an electronics course. The first property is the simplicity of the functions’ representation and implementation; the essence of a threshold function is understandable on the common sense level. The second property is the dual analog-digital nature of the threshold functions. The definition of a threshold function usually includes both Boolean and arithmetic portions and weaves together the two alternative domains: digital and analog. Since students are familiar with regular arithmetic functions from previous math courses, the addition of Boolean concepts is simple to grasp. The possibility to transform any threshold function from one domain to another, serves as a powerful tool for processes teaching. The third property we consider is the multiple representations possible for threshold functions. Besides the classical Boolean and arithmetic representations, a threshold function can be represented in the format of an electric/electronic circuit and also can be represented in a spatial form, by three-dimensional visualization for better understanding the functional properties of threshold functions. The paper discusses a problem-based learning with two main types of problems: synthesis and analysis problems of threshold elements. While the analysis problem is relatively simple, the problem of optimal synthesis is NP-complete, and equivalent to a well-known optimization problem that exists also in linear programming. Using the linear programming for teaching the synthesis of a threshold element is a challenging pedagogical task. The paper describes an approach for solving this task. A number of real-world problems may be formulated and efficiently solved by using the proposed threshold-based approach, for example the problems of event-driven control, fuzzy control, linear optimization, self-regulation. These problems formulate as students’ assignments, and are used in the lesson. These exercises convert a lesson of electronics into an interesting, challengeable and useful educational event. Introduction of the threshold approach into the electronics curriculum enables the students to acquire much deeper understanding of electronic systems.
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Schnieber, Martha, Saman Froehlich, and Rolf Drechsler. "Depth Optimized Synthesis of Symmetric Boolean Functions." In 2021 IEEE Computer Society Annual Symposium on VLSI (ISVLSI). IEEE, 2021. http://dx.doi.org/10.1109/isvlsi51109.2021.00022.

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Beg, Azam, P. W. C. Prasad, Walid Ibrahim, and Emad Abu Shama. "Utilizing synthesis to verify Boolean function models." In 2008 IEEE International Symposium on Circuits and Systems - ISCAS 2008. IEEE, 2008. http://dx.doi.org/10.1109/iscas.2008.4541733.

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