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Academic literature on the topic 'Propositional satisfiability problems'

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Journal articles on the topic "Propositional satisfiability problems"

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Jeroslow, Robert G., and Jinchang Wang. "Solving propositional satisfiability problems." Annals of Mathematics and Artificial Intelligence 1, no. 1-4 (September 1990): 167–87. http://dx.doi.org/10.1007/bf01531077.

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MEIER, ARNE, MICHAEL THOMAS, HERIBERT VOLLMER, and MARTIN MUNDHENK. "THE COMPLEXITY OF SATISFIABILITY FOR FRAGMENTS OF CTL AND CTL⋆." International Journal of Foundations of Computer Science 20, no. 05 (October 2009): 901–18. http://dx.doi.org/10.1142/s0129054109006954.

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The satisfiability problems for [Formula: see text] and [Formula: see text] are known to be EXPTIME-complete, resp. 2EXPTIME-complete (Fischer and Ladner (1979), Vardi and Stockmeyer (1985)). For fragments that use less temporal or propositional operators, the complexity may decrease. This paper undertakes a systematic study of satisfiability for [Formula: see text]-and [Formula: see text]-formulae over restricted sets of propositional and temporal operators. We show that restricting the temporal operators yields satisfiability problems complete for 2EXPTIME, EXPTIME, PSPACE, and NP. Restricting the propositional operators either does not change the complexity (as determined by the temporal operators), or yields very low complexity like NC1, TC0, or NLOGTIME.
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MOUHOUB, MALEK, and SAMIRA SADAOUI. "SOLVING INCREMENTAL SATISFIABILITY." International Journal on Artificial Intelligence Tools 16, no. 01 (February 2007): 139–47. http://dx.doi.org/10.1142/s0218213007003254.

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Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of "polynomial-time reducibility" all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique while the approximation methods rely on stochastic local search and genetic algorithms. Experimental tests, conducted on randomly generated SAT instances, demonstrate the efficiency in time of the approximation methods over the branch and bound algorithm. However these approximation methods do not always guarantee the completeness of the solution returned. We show that a method we propose that uses non systematic search in a limited form together with branch and bound has the best compromise, in practice, between time and quality of the solution returned (success ratio).
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Aravantinos, V., R. Caferra, and N. Peltier. "Decidability and Undecidability Results for Propositional Schemata." Journal of Artificial Intelligence Research 40 (March 22, 2011): 599–656. http://dx.doi.org/10.1613/jair.3351.

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We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability.
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Cameron, Chris, Rex Chen, Jason Hartford, and Kevin Leyton-Brown. "Predicting Propositional Satisfiability via End-to-End Learning." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 3324–31. http://dx.doi.org/10.1609/aaai.v34i04.5733.

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Strangely enough, it is possible to use machine learning models to predict the satisfiability status of hard SAT problems with accuracy considerably higher than random guessing. Existing methods have relied on extensive, manual feature engineering and computationally complex features (e.g., based on linear programming relaxations). We show for the first time that even better performance can be achieved by end-to-end learning methods — i.e., models that map directly from raw problem inputs to predictions and take only linear time to evaluate. Our work leverages deep network models which capture a key invariance exhibited by SAT problems: satisfiability status is unaffected by reordering variables and clauses. We showed that end-to-end learning with deep networks can outperform previous work on random 3-SAT problems at the solubility phase transition, where: (1) exactly 50% of problems are satisfiable; and (2) empirical runtimes of known solution methods scale exponentially with problem size (e.g., we achieved 84% prediction accuracy on 600-variable problems, which take hours to solve with state-of-the-art methods). We also showed that deep networks can generalize across problem sizes (e.g., a network trained only on 100-variable problems, which typically take about 10 ms to solve, achieved 81% accuracy on 600-variable problems).
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Reith, Steffen, and Heribert Vollmer. "Optimal satisfiability for propositional calculi and constraint satisfaction problems." Information and Computation 186, no. 1 (October 2003): 1–19. http://dx.doi.org/10.1016/s0890-5401(03)00092-0.

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MOUHOUB, MALEK. "SYSTEMATIC VERSUS LOCAL SEARCH AND GA TECHNIQUES FOR INCREMENTAL SAT." International Journal of Computational Intelligence and Applications 07, no. 01 (March 2008): 77–96. http://dx.doi.org/10.1142/s1469026808002193.

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Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of "polynomial-time reducibility" all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique, whereas the approximation methods rely on stochastic local search (SLS) and genetic algorithms (GAs). A comprehensive empirical study, conducted on a wide range of randomly generated consistent SAT instances, demonstrates the efficiency in time of the approximation methods over the branch and bound algorithm. However, these approximation methods do not guarantee the completeness of the solution returned. We show that a method we propose that uses nonsystematic search in a limited form together with branch and bound has the best compromise, in practice, between time and the success ratio (percentage of instances completely solved).
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Balu, Radhakrishnan, Dale Shires, and Raju Namburu. "A quantum algorithm for uniform sampling of models of propositional logic based on quantum probability." Journal of Defense Modeling and Simulation: Applications, Methodology, Technology 16, no. 1 (May 17, 2016): 57–65. http://dx.doi.org/10.1177/1548512916648232.

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We describe a class of quantum algorithms to generate models of propositional logic with equal probability. We consider quantum stochastic flows that are the quantum analogues of classical Markov chains and establish a relation between fixed points on the two flows. We construct chains inspired by von Neumann algorithms using uniform measures as fixed points to construct the corresponding irreversible quantum stochastic flows. We formulate sampling models of propositions in the framework of adiabatic quantum computing and solve the underlying satisfiability instances. Satisfiability formulation is an important and successful technique in modeling the decision theoretic problems in a classical context. We discuss some features of the proposed algorithms tested on an existing quantum annealer D-Wave II extending the simulation of decision theoretic problems to a quantum context.
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Pinkas, Gadi. "Symmetric Neural Networks and Propositional Logic Satisfiability." Neural Computation 3, no. 2 (June 1991): 282–91. http://dx.doi.org/10.1162/neco.1991.3.2.282.

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Connectionist networks with symmetric weights (like Hopfield networks and Boltzmann Machines) use gradient descent to find a minimum for quadratic energy functions. We show equivalence between the problem of satisfiability in propositional calculus and the problem of minimizing those energy functions. The equivalence is in the sense that for any satisfiable well-formed formula (WFF) we can find a quadratic function that describes it, such that the set of solutions that minimizes the function is equal to the set of truth assignments that satisfy the WFF. We also show that in the same sense every quadratic energy function describes some satisfiable WFF. Algorithms are given to transform any propositional WFF into an energy function that describes it and vice versa. High-order models that use sigma-pi units are shown to be equivalent to the standard quadratic models with additional hidden units. An algorithm to convert high-order networks to low-order ones is used to implement a satisfiability problem-solver on a connectionist network. The results give better understanding of the role of hidden units and of the limitations and capabilities of symmetric connectionist models. The techniques developed for the satisfiability problem may be applied to a wide range of other problems, such as associative memories, finding maximal consistent subsets, automatic deduction, and even nonmonotonic reasoning.
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Boudane, Abdelhamid, Saïd Jabbour, Lakhdar Sais, and Yakoub Salhi. "SAT-Based Data Mining." International Journal on Artificial Intelligence Tools 27, no. 01 (February 2018): 1840002. http://dx.doi.org/10.1142/s021821301840002x.

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Several propositional satisfiability (SAT) based encodings have been proposed to deal with various data mining problems including itemset and sequence mining problems. This research issue allows to model data mining problems in a declarative way, while exploiting efficient SAT solving techniques. In this paper, we overview our contributions on the application of propositional satisfiability (SAT) to model and solve itemset mining tasks. We first present a SAT based encoding of frequent closed itemset mining task as a propositional formula whose models corresponds to the patterns to be mined. Secondly, we show that some data mining constraints can be avoided by reformulation. We illustrate this issue by reformulating the closeness constraint using the notion of minimal models. Finally, we also addressed the scalability issue, one of the most important challenge of these nice declarative framework. To this end, we proposed a complete partition based approach whose aim is to avoid encoding the whole database as a single formula. Using a partition on the set of items, our new approach leads to several propositional formulas of reasonable size. The experimental evaluation on several known datasets shows huge improvements in comparison to the direct approach without partitioning, while reducing significantly the performance gap with respect to specialized algorithms.
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Dissertations / Theses on the topic "Propositional satisfiability problems"

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Pham, Duc Nghia, and n/a. "Modelling and Exploiting Structures in Solving Propositional Satisfiability Problems." Griffith University. Institute for Integrated and Intelligent Systems, 2006. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20070216.143447.

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Recent research has shown that it is often preferable to encode real-world problems as propositional satisfiability (SAT) problems and then solve using a general purpose SAT solver. However, much of the valuable information and structure of these realistic problems is flattened out and hidden inside the corresponding Conjunctive Normal Form (CNF) encodings of the SAT domain. Recently, systematic SAT solvers have been progressively improved and are now able to solve many highly structured practical problems containing millions of clauses. In contrast, state-of-the-art Stochastic Local Search (SLS) solvers still have difficulty in solving structured problems, apparently because they are unable to exploit hidden structure as well as the systematic solvers. In this thesis, we study and evaluate different ways to effectively recognise, model and efficiently exploit useful structures hidden in realistic problems. A summary of the main contributions is as follows: 1. We first investigate an off-line processing phase that applies resolution-based pre-processors to input formulas before running SLS solvers on these problems. We report an extensive empirical examination of the impact of SAT pre-processing on the performance of contemporary SLS techniques. It emerges that while all the solvers examined do indeed benefit from pre-processing, the effects of different pre-processors are far from uniform across solvers and across problems. Our results suggest that SLS solvers need to be equipped with multiple pre-processors if they are ever to match the performance of systematic solvers on highly structured problems. [Part of this study was published at the AAAI-05 conference]. 2. We then look at potential approaches to bridging the gap between SAT and constraint satisfaction problem (CSP) formalisms. One approach has been to develop a many-valued SAT formalism (MV-SAT) as an intermediate paradigm between SAT and CSP, and then to translate existing highly efficient SAT solvers to the MV-SAT domain. In this study, we follow a different route, developing SAT solvers that can automatically recognise CSP structure hidden in SAT encodings. This allows us to look more closely at how constraint weighting can be implemented in the SAT and CSP domains. Our experimental results show that a SAT-based mechanism to handle weights, together with a CSP-based method to instantiate variables, is superior to other combinations of SAT and CSP-based approaches. In addition, SLS solvers based on this many-valued weighting approach outperform other existing approaches to handle many-valued CSP structures. [Part of this study was published at the AAAI-05 conference]. 3. Finally, we propose and evaluate six different schemes to encode temporal reasoning problems, in particular the Interval Algebra (IA) networks, into SAT CNF formulas. We then empirically examine the performance of local search as well as systematic solvers on the new temporal SAT representations, in comparison with solvers that operate on native IA representations. Our empirical results show that zChaff (a state-of-the-art complete SAT solver) together with the best IA-to-SAT encoding scheme, can solve temporal problems significantly faster than existing IA solvers working on the equivalent native IA networks. [Part of this study was published at the CP-05 workshop].
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Pham, Duc Nghia. "Modelling and Exploiting Structures in Solving Propositional Satisfiability Problems." Thesis, Griffith University, 2006. http://hdl.handle.net/10072/365503.

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Recent research has shown that it is often preferable to encode real-world problems as propositional satisfiability (SAT) problems and then solve using a general purpose SAT solver. However, much of the valuable information and structure of these realistic problems is flattened out and hidden inside the corresponding Conjunctive Normal Form (CNF) encodings of the SAT domain. Recently, systematic SAT solvers have been progressively improved and are now able to solve many highly structured practical problems containing millions of clauses. In contrast, state-of-the-art Stochastic Local Search (SLS) solvers still have difficulty in solving structured problems, apparently because they are unable to exploit hidden structure as well as the systematic solvers. In this thesis, we study and evaluate different ways to effectively recognise, model and efficiently exploit useful structures hidden in realistic problems. A summary of the main contributions is as follows: 1. We first investigate an off-line processing phase that applies resolution-based pre-processors to input formulas before running SLS solvers on these problems. We report an extensive empirical examination of the impact of SAT pre-processing on the performance of contemporary SLS techniques. It emerges that while all the solvers examined do indeed benefit from pre-processing, the effects of different pre-processors are far from uniform across solvers and across problems. Our results suggest that SLS solvers need to be equipped with multiple pre-processors if they are ever to match the performance of systematic solvers on highly structured problems. [Part of this study was published at the AAAI-05 conference]. 2. We then look at potential approaches to bridging the gap between SAT and constraint satisfaction problem (CSP) formalisms. One approach has been to develop a many-valued SAT formalism (MV-SAT) as an intermediate paradigm between SAT and CSP, and then to translate existing highly efficient SAT solvers to the MV-SAT domain. In this study, we follow a different route, developing SAT solvers that can automatically recognise CSP structure hidden in SAT encodings. This allows us to look more closely at how constraint weighting can be implemented in the SAT and CSP domains. Our experimental results show that a SAT-based mechanism to handle weights, together with a CSP-based method to instantiate variables, is superior to other combinations of SAT and CSP-based approaches. In addition, SLS solvers based on this many-valued weighting approach outperform other existing approaches to handle many-valued CSP structures. [Part of this study was published at the AAAI-05 conference]. 3. Finally, we propose and evaluate six different schemes to encode temporal reasoning problems, in particular the Interval Algebra (IA) networks, into SAT CNF formulas. We then empirically examine the performance of local search as well as systematic solvers on the new temporal SAT representations, in comparison with solvers that operate on native IA representations. Our empirical results show that zChaff (a state-of-the-art complete SAT solver) together with the best IA-to-SAT encoding scheme, can solve temporal problems significantly faster than existing IA solvers working on the equivalent native IA networks. [Part of this study was published at the CP-05 workshop].
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
Institute for Integrated and Intelligent Systems
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Duong, Thach-Thao Nguyen. "Improving Diversification in Local Search for Propositional Satisfiability." Thesis, Griffith University, 2014. http://hdl.handle.net/10072/365717.

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In recent years, the Propositional Satisfiability (SAT) has become standard for encoding real world complex constrained problems. SAT has significant impacts on various research fields in Artificial Intelligence (AI) and Constraint Programming (CP). SAT algorithms have also been successfully used in solving many practical and industrial applications that include electronic design automation, default reasoning, diagnosis, planning, scheduling, image interpretation, circuit design, and hardware and software verification. The most common representation of a SAT formula is the Conjunctive Normal Form (CNF). A CNF formula is a conjunction of clauses where each clause is a disjunction of Boolean literals. A SAT formula is satisfiable if there is a truth assignment for each variable such that all clauses in the formula are satisfied. Solving a SAT problem is to determine a truth assignment that satisfies a CNF formula. SAT is the first problem proved to be NP-complete [20]. There are many algorithmic methodologies to solve SAT. The most obvious one is systematic search; however another popular and successful approach is stochastic local search (SLS). Systematic search is usually referred to as complete search or backtrack-style search. In contrast, SLS is a method to explore the search space by randomisation and perturbation operations. Although SLS is an incomplete search method, it is able to find the solutions effectively by using limited time and resources. Moreover, some SLS solvers can solve hard SAT problems in a few minutes while these problems could be beyond the capacity of systematic search solvers.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Information and Communication Technology
Science, Environment, Engineering and Technology
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Ishtaiwi, Abdelraouf. "Towards Effective Parameter-Free Clause Weighting Local Search for SAT." Thesis, Griffith University, 2008. http://hdl.handle.net/10072/366980.

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Recent research has shown that it is often preferable to encode real-world problems as propositional satisfiability (SAT) problems, and then solve them using general purpose SAT solvers. However, most SAT solvers require the tuning of parameters in order to obtain optimum performance. Tuning these parameters usually takes a considerable amount of time, and even to achieve average performance can require many runs with many different parameter settings. In this thesis we investigate various ways to improve the overall performance of local search solvers via new techniques that do not employ parameters and therefore take considerably less time for experimentation...
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
Institute for Integrated and Intelligent Systems
Faculty of Engineering and Information Technology
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5

Slater, Andrew, and andrew slater@csl anu edu au. "Investigations into Satisfiability Search." The Australian National University. Research School of Information Sciences and Engineering, 2003. http://thesis.anu.edu.au./public/adt-ANU20040310.103258.

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In this dissertation we investigate theoretical aspects of some practical approaches used in solving and understanding search problems. We concentrate on the Satisfiability problem, which is a strong representative from search problem domains. The work develops general theoretical foundations to investigate some practical aspects of satisfiability search. This results in a better understanding of the fundamental mechanics for search algorithm construction and behaviour. A theory of choice or branching heuristics is presented, accompanied by results showing a correspondence of both parameterisations and performance when the method is compared to previous empirically motivated branching techniques. The logical foundations of the backtracking mechanism are explored alongside formulations for reasoning in relevant logics which results in the development of a malleable backtracking mechanism that subsumes other intelligent backtracking proof construction techniques and allows the incorporation of proof rearrangement strategies. Moreover, empirical tests show that relevant backtracking outperforms all other forms of intelligent backtracking search tree construction methods. An investigation into modelling and generating world problem instances justifies a modularised problem model proposal which is used experimentally to highlight the practicability of search algorithms for the proposed model and related domains.
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Drake, Lyndon Paul. "Combining inference and backtracking search for the propositional satisfiability problem." Thesis, University of York, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421496.

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Slater, Andrew. "Investigations into Satisfiability Search." Phd thesis, 2004. http://hdl.handle.net/1885/48193.

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In this dissertation we investigate theoretical aspects of some practical approaches used in solving and understanding search problems. We concentrate on the Satisfiability problem, which is a strong representative from search problem domains. The work develops general theoretical foundations to investigate some practical aspects of satisfiability search. This results in a better understanding of the fundamental mechanics for search algorithm construction and behaviour. A theory of choice or branching heuristics is presented, accompanied by results showing a correspondence of both parameterisations and performance when the method is compared to previous empirically motivated branching techniques. The logical foundations of the backtracking mechanism are explored alongside formulations for reasoning in relevant logics which results in the development of a malleable backtracking mechanism that subsumes other intelligent backtracking proof construction techniques and allows the incorporation of proof rearrangement strategies. Moreover, empirical tests show that relevant backtracking outperforms all other forms of intelligent backtracking search tree construction methods. An investigation into modelling and generating world problem instances justifies a modularised problem model proposal which is used experimentally to highlight the practicability of search algorithms for the proposed model and related domains.
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"A solution scheme of satisfiability problem by active usage of totally unimodularity property." 2003. http://library.cuhk.edu.hk/record=b5896100.

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by Mei Long.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 93-98).
Abstracts in English and Chinese.
Table of Contents --- p.v
Abstract --- p.viii
Acknowledgements --- p.x
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Satisfiability Problem --- p.1
Chapter 1.2 --- Motivation of the Research --- p.1
Chapter 1.3 --- Overview of the Thesis --- p.2
Chapter 2 --- Satisfiability Problem --- p.4
Chapter 2.1 --- Satisfiability Problem --- p.5
Chapter 2.1.1 --- Basic Definition --- p.5
Chapter 2.1.2 --- Phase Transitions --- p.5
Chapter 2.2 --- History --- p.6
Chapter 2.3 --- The Basic Search Algorithm --- p.8
Chapter 2.4 --- Some Improvements to the Basic Algorithm --- p.9
Chapter 2.4.1 --- Satz by Chu-Min Li --- p.9
Chapter 2.4.2 --- Heuristics and Local Search --- p.12
Chapter 2.4.3 --- Relaxation --- p.13
Chapter 2.5 --- Benchmarks --- p.14
Chapter 2.5.1 --- Specific Problems --- p.14
Chapter 2.5.2 --- Randomly Generated Problems --- p.14
Chapter 2.6 --- Software and Internet Information for SAT solving --- p.16
Chapter 2.6.1 --- Stochastic Local Search Algorithms (incomplete) --- p.16
Chapter 2.6.2 --- Systematic Search Algorithms (complete) --- p.16
Chapter 2.6.3 --- Some useful Links to SAT Related Sites --- p.17
Chapter 3 --- Integer Programming Formulation for Logic Problem --- p.18
Chapter 3.1 --- SAT Problem --- p.19
Chapter 3.2 --- MAXSAT Problem --- p.19
Chapter 3.3 --- Logical Inference Problem --- p.19
Chapter 3.4 --- Weighted Exact Satisfiability Problem --- p.20
Chapter 4 --- Integer Programming Formulation for SAT Problem --- p.22
Chapter 4.1 --- From 3-CNF SAT Clauses to Zero-One IP Constraints --- p.22
Chapter 4.2 --- Integer Programming Model for 3-SAT --- p.23
Chapter 4.3 --- The Equivalence of the SAT and the IP --- p.23
Chapter 4.4 --- Example --- p.24
Chapter 5 --- Integer Solvability of Linear Programs --- p.27
Chapter 5.1 --- Unimodularity --- p.27
Chapter 5.2 --- Totally Unimodularity --- p.28
Chapter 5.3 --- Some Results on Recognition of Linear Solvability of IP --- p.32
Chapter 6 --- TU Based Matrix Research Results --- p.33
Chapter 6.1 --- 2x2 Matrix's TU Property --- p.33
Chapter 6.2 --- Extended Integer Programming Model for SAT --- p.34
Chapter 6.3 --- 3x3 Matrix's TU Property --- p.35
Chapter 7 --- Totally Unimodularity Based Branching-and-Bound Algorithm --- p.38
Chapter 7.1 --- Introduction --- p.38
Chapter 7.1.1 --- Enumeration Trees --- p.39
Chapter 7.1.2 --- The Concept of Branch and Bound --- p.42
Chapter 7.2 --- TU Based Branching Rule --- p.43
Chapter 7.2.1 --- How to sort variables based on 2x2 submatrices --- p.43
Chapter 7.2.2 --- How to sort the rest variables --- p.45
Chapter 7.3 --- TU Based Bounding Rule --- p.46
Chapter 7.4 --- TU Based Branch-and-Bound Algorithm --- p.47
Chapter 7.5 --- Example --- p.49
Chapter 8 --- Numerical Result --- p.57
Chapter 8.1 --- Experimental Result --- p.57
Chapter 8.2 --- Statistical Results of ILOG CPLEX --- p.59
Chapter 9 --- Conclusions --- p.61
Chapter 9.1 --- Contributions --- p.61
Chapter 9.2 --- Future Work --- p.62
Chapter A --- The Coefficient Matrix A for Example in Chapter 7 --- p.64
Chapter B --- The Detailed Numerical Information of Solution Process for Exam- ple in Chapter 7 --- p.66
Chapter C --- Experimental Result --- p.67
Chapter C.1 --- "# of variables: 20, # of clauses: 91" --- p.67
Chapter C.2 --- "# of variables: 50, # of clauses: 218" --- p.70
Chapter C.3 --- # of variables: 75，# of clauses: 325 --- p.73
Chapter C.4 --- "# of variables: 100, # of clauses: 430" --- p.76
Chapter D --- Experimental Result of ILOG CPLEX --- p.80
Chapter D.1 --- # of variables: 20´ة # of clauses: 91 --- p.80
Chapter D.2 --- # of variables: 50，#of clauses: 218 --- p.83
Chapter D.3 --- # of variables: 75，# of clauses: 325 --- p.86
Chapter D.4 --- "# of variables: 100, # of clauses: 430" --- p.89
Bibliography --- p.93
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Χαρατσάρης, Δημήτριος. "Υλοποίηση διαδικτυακού προσομοιωτή για αλγορίθμους επίλυσης προβλημάτων SAT." Thesis, 2012. http://hdl.handle.net/10889/5754.

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Η παρούσα διπλωµατική εργασία ασχολείται με το θέμα των Αλγορίθμων Επίλυσης Προβληµάτων SAT. Η εργασία αυτή εκπονήθηκε στα πλαίσια του Εργαστηρίου Ενσύρµατης Επικοινωνίας του Τµήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του Πανεπιστηµίου Πατρών. Σκοπός της είναι η δημιουργία ενός Προσομοιωτή των αλγορίθμων αυτών, ο οποίος να μπορεί να προσπελαστεί από οποιονδήποτε μέσω του διαδικτύου. Αρχικά έγινε µία εισαγωγή στο αντικείμενο της Τεχνητής Νοημοσύνης και πιο συγκεκριµένα στην Προτασιακή Λογική, ενώ δόθηκε και το απαραίτητο υπόβαθρο για να κατανοηθεί το πρόβληµμα και οι τεχνικές λύσης του. Τέλος, επιλέχθηκε να γίνει η υλοποίηση του Προσωμοιωτή σε Java.
This diploma dissertation deals with SAT solvers, algorithms for the Boolean satisfiability problem. It was produced in the Wire Communications Laboratory of the Electrical and Computer Engineering Department of the University of Patras. Its aim is to create a simulator for these algorithms, accessible to anyone via the Internet. An introduction to the field of Artificial Intelligence and more specifically to Propositional Calculus was given as well as the necessary groundwork to understand the problem and its solution approaches. The simulation implementation was developed in Java
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Books on the topic "Propositional satisfiability problems"

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Harris, J. G. Approaches to the satisfiability problem of propositional logic. Manchester: UMIST, 1994.

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Dingzhu, Du, Gu Jun 1956-, Pardalos P. M. 1954-, and NSF Science and Technology Center in Discrete Mathematics and Theoretical Computer Science., eds. Satisfiability problem: Theory and applications : DIMACS workshop, March 11-13, 1996. Providence, R.I: American Mathematical Society, 1997.

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van, Dieter Melkebeek. A Survey of Lower Bounds for Satisfiability and Related Problems. Now Publishers Inc, 2007.

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The satisfiability problem. Amsterdam: Elsevier, 1999.

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Book chapters on the topic "Propositional satisfiability problems"

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de Haan, Ronald. "Problems Related to Propositional Satisfiability." In Parameterized Complexity in the Polynomial Hierarchy, 205–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. http://dx.doi.org/10.1007/978-3-662-60670-4_10.

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Graça, Ana, João Marques-Silva, and Inês Lynce. "Haplotype Inference Using Propositional Satisfiability." In Mathematical Approaches to Polymer Sequence Analysis and Related Problems, 127–47. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6800-5_7.

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Reith, Steffen, and Heribert Vollmer. "Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems." In Lecture Notes in Computer Science, 640–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44612-5_59.

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Guller, Dušan. "On the Satisfiability and Validity Problems in the Propositional Gödel Logic." In Studies in Computational Intelligence, 211–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27534-0_14.

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Tang, Daijue, Yinlei Yu, Darsh Ranjan, and Sharad Malik. "Analysis of Search Based Algorithms for Satisfiability of Propositional and Quantified Boolean Formulas Arising from Circuit State Space Diameter Problems." In Theory and Applications of Satisfiability Testing, 292–305. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11527695_23.

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Wang, Jinchang. "Branching rules for propositional satisfiability test." In Satisfiability Problem: Theory and Applications, 351–64. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/dimacs/035/09.

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Plaisted, Daivd, and Geoffrey Alexander. "Propositional search efficiency and first-order theorem proving." In Satisfiability Problem: Theory and Applications, 335–50. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/dimacs/035/08.

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Aravantinos, Vincent, Ricardo Caferra, and Nicolas Peltier. "Complexity of the Satisfiability Problem for a Class of Propositional Schemata." In Language and Automata Theory and Applications, 58–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13089-2_5.

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Arvind, V., and S. Biswas. "On certain bandwidth restricted versions of the satisfiability problem of propositional CNF formulas." In Lecture Notes in Computer Science, 456–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-18625-5_68.

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Sanders, Peter, and Dominik Schreiber. "Decentralized Online Scheduling of Malleable NP-hard Jobs." In Euro-Par 2022: Parallel Processing, 119–35. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12597-3_8.

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AbstractIn this work, we address an online job scheduling problem in a large distributed computing environment. Each job has a priority and a demand of resources, takes an unknown amount of time, and is malleable, i.e., the number of allotted workers can fluctuate during its execution. We subdivide the problem into (a) determining a fair amount of resources for each job and (b) assigning each job to an according number of processing elements. Our approach is fully decentralized, uses lightweight communication, and arranges each job as a binary tree of workers which can grow and shrink as necessary. Using the NP-complete problem of propositional satisfiability (SAT) as a case study, we experimentally show on up to 128 machines (6144 cores) that our approach leads to near-optimal utilization, imposes minimal computational overhead, and performs fair scheduling of incoming jobs within a few milliseconds.
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Conference papers on the topic "Propositional satisfiability problems"

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Ignatiev, Alexey, Antonio Morgado, and Joao Marques-Silva. "Cardinality Encodings for Graph Optimization Problems." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/91.

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Different optimization problems defined on graphs find application in complex network analysis. Existing propositional encodings render impractical the use of propositional satisfiability (SAT) and maximum satisfiability (MaxSAT) solvers for solving a variety of these problems on large graphs. This paper has two main contributions. First, the paper identifies sources of inefficiency in existing encodings for different optimization problems in graphs. Second, for the concrete case of the maximum clique problem, the paper develops a novel encoding which is shown to be far more compact than existing encodings for large sparse graphs. More importantly, the experimental results show that the proposed encoding enables existing SAT solvers to compute a maximum clique for large sparse networks, often more efficiently than the state of the art.
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Caleiro, Carlos, Filipe Casal, and Andreia Mordido. "Classical Generalized Probabilistic Satisfiability." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/126.

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We analyze a classical generalized probabilistic satisfiability problem (GGenPSAT) which consists in deciding the satisfiability of Boolean combinations of linear inequalities involving probabilities of classical propositional formulas. GGenPSAT coincides precisely with the satisfiability problem of the probabilistic logic of Fagin et al. and was proved to be NP-complete. Here, we present a polynomial reduction of GGenPSAT to SMT over the quantifier-free theory of linear integer and real arithmetic. Capitalizing on this translation, we implement and test a solver for the GGenPSAT problem. As previously observed for many other NP-complete problems, we are able to detect a phase transition behavior for GGenPSAT.
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Lee, Nian-Ze, Yen-Shi Wang, and Jie-Hong R. Jiang. "Solving Stochastic Boolean Satisfiability under Random-Exist Quantification." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/96.

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Stochastic Boolean Satisfiability (SSAT) is a powerful formalism to represent computational problems with uncertainly, such as belief network inference and propositional probabilistic planning. Solving SSAT formulas lies in the same complexity class (PSPACE-complete) as solving Quantified Boolean Formula (QBF). While many endeavors have been made to enhance QBF solving, SSAT has drawn relatively less attention in recent years. This paper focuses on random-exist quantified SSAT formulas, and proposes an algorithm combining binary decision diagram (BDD), logic synthesis, and modern SAT techniques to improve computational efficiency. Unlike prior exact SSAT algorithms, the proposed method can be easily modified to solve approximate SSAT by deriving upper and lower bounds of satisfying probability. Experimental results show that our method outperforms the state-of-the-art algorithm on random k-CNF formulas and has effective application to approximate SSAT on circuit benchmarks.
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Cordeiro, Lucas C. "Exploiting the SAT Revolution for Automated Software Verification: Report from an Industrial Case Study." In Anais Estendidos do Latin-American Symposium on Dependable Computing. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ladc.2021.18531.

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In the last three decades, Boolean Satisfiability (SAT) solvers experienced a dramatic performance revolution; they are now used as the backend of various industrial verification engines. SAT solvers can now check logical formulas that contain millions of propositional variables. In Satisfiability Modulo Theories (SMT) solvers, predicates from various theories are not encoded using propositional variables as in SAT but remain in the problem formulation. Thus, SMT solvers can be used as backends for solving the generated verification conditions to cope with increasing software complexity from industrial applications. This talk will overview automated software verification techniques that rely on sophisticated SMT solvers built over efficient SAT solvers. I will discuss challenges, problems, and recent advances to ensure safety and security in open-source and embedded software applications. I will describe novel algorithms that exploit fuzzing, explicit-state, and SMT-based symbolic model checking for verifying single- and multi-threaded software. These algorithms were the first to verify multi-threaded C/Posix software based on shared-memory synchronization and communication symbolically. They are implemented in industrial-strength software verification tools, now considered state-of-the-art in the software testing and verification community, receiving 28 medals at SV-COMP and Test-COMP. This achievement enabled industrial research collaborations with Intel and Nokia. Software engineers applied these tools to find real security vulnerabilities in large-scale software systems (e.g., memory safety in firmware for Intel and arithmetic overflow in telecommunication software for Nokia, neither of which had been found before).
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Kolb, Samuel, Stefano Teso, Andrea Passerini, and Luc De Raedt. "Learning SMT(LRA) Constraints using SMT Solvers." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/323.

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We introduce the problem of learning SMT(LRA) constraints from data. SMT(LRA) extends propositional logic with (in)equalities between numerical variables. Many relevant formal verification problems can be cast as SMT(LRA) instances and SMT(LRA) has supported recent developments in optimization and counting for hybrid Boolean and numerical domains. We introduce SMT(LRA) learning, the task of learning SMT(LRA) formulas from examples of feasible and infeasible instances, and we contribute INCAL, an exact non-greedy algorithm for this setting. Our approach encodes the learning task itself as an SMT(LRA) satisfiability problem that can be solved directly by SMT solvers. INCAL is an incremental algorithm that achieves exact learning by looking only at a small subset of the data, leading to significant speed-ups. We empirically evaluate our approach on both synthetic instances and benchmark problems taken from the SMT-LIB benchmarks repository.
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Grossi, Davide, Emiliano Lorini, and François Schwarzentruber. "The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/710.

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We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.
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Zou, Li, and Wenjiang Li. "Satisfiability Problem of Linguistic Truth-Valued Intuitionistic Propositional Logic." In 2008 3rd International Conference on Innovative Computing Information and Control. IEEE, 2008. http://dx.doi.org/10.1109/icicic.2008.485.

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Herzig, Andreas, Frédéric Maris, and Julien Vianey. "Dynamic logic of parallel propositional assignments and its applications to planning." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/774.

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We introduce a dynamic logic with parallel composition and two kinds of nondeterministic composition, exclusive and inclusive. We show PSPACE completeness of both the model checking and the satisfiability problem and apply our logic to sequential and parallel classical planning where actions have conditional effects.
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Liang, Jiaxin, Feifei Ma, Junping Zhou, and Minghao Yin. "AllSATCC: Boosting AllSAT Solving with Efficient Component Analysis." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/259.

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All Solution SAT (AllSAT) is a variant of Propositional Satisfiability, which aims to find all satisfying assignments for a given formula. AllSAT has significant applications in different domains, such as software testing, data mining, and network verification. In this paper, observing that the lack of component analysis may result in more work for algorithms with non-chronological backtracking, we propose a DPLL-based algorithm for solving AllSAT problem, named AllSATCC, which takes advantage of component analysis to reduce work repetition caused by non-chronological backtracking. The experimental results show that our algorithm outperforms the state-of-the-art algorithms on most instances.
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Geatti, Luca, Alessandro Gianola, and Nicola Gigante. "Linear Temporal Logic Modulo Theories over Finite Traces." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/366.

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This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic, called LTLf Modulo Theories (LTLfMT), is semi-decidable. Nevertheless, its high expressiveness comes useful in a number of use cases, such as model-checking of data-aware processes and data-aware planning. Despite the general undecidability of these problems, being able to solve satisfiable instances is a compromise worth studying. After motivating and describing such use cases, we provide a sound and complete semi-decision procedure for LTLfMT based on the SMT encoding of a one-pass tree-shaped tableau system. The algorithm is implemented in the BLACK satisfiability checking tool, and an experimental evaluation shows the feasibility of the approach on novel benchmarks.
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Reports on the topic "Propositional satisfiability problems"

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Baader, Franz, and Barbara Morawska. SAT Encoding of Unification in EL. Technische Universität Dresden, 2010. http://dx.doi.org/10.25368/2022.177.

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The Description Logic EL is an inexpressive knowledge representation language, which nevertheless has recently drawn considerable attention in the knowledge representation and the ontology community since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in EL is NP-complete, and thus of a complexity that is considerably lower than in other Description Logics of comparably restricted expressive power. In this paper, we introduce a new NP-algorithm for solving unification problem in EL, which is based on a reduction to satisfiability in propositional logic (SAT). The advantage of this new algorithm is, on the one hand, that it allows us to employ highly optimized state of the art SAT solverswhen implementing an EL-unification algorithm. On the other hand, this reduction provides us with a proof of the fact that EL-unification is in NP that is much simpler than the one given in our previous paper on EL-unification.
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Borgwardt, Stefan, Marcel Lippmann, and Veronika Thost. Reasoning with Temporal Properties over Axioms of DL-Lite. Technische Universität Dresden, 2014. http://dx.doi.org/10.25368/2022.208.

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Recently, a lot of research has combined description logics (DLs) of the DL-Lite family with temporal formalisms. Such logics are proposed to be used for situation recognition and temporalized ontology-based data access. In this report, we consider DL-Lite-LTL, in which axioms formulated in a member of the DL-Lite family are combined using the operators of propositional linear-time temporal logic (LTL). We consider the satisfiability problem of this logic in the presence of so-called rigid symbols whose interpretation does not change over time. In contrast to more expressive temporalized DLs, the computational complexity of this problem is the same as for LTL, even w.r.t. rigid symbols.
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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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