Relevant bibliographies by topics / Probabilistic preorder

Academic literature on the topic 'Probabilistic preorder'

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Published: 11 March 2023

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Journal articles on the topic "Probabilistic preorder"

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BAIER, CHRISTEL, and MARTA KWIATKOWSKA. "Domain equations for probabilistic processes." Mathematical Structures in Computer Science 10, no. 6 (December 2000): 665–717. http://dx.doi.org/10.1017/s0960129599002984.

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In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We define operational notions of preorder and equivalence as probabilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solving domain equations to the probabilistic case and give two denotational semantics for the calculus. The first, ‘smooth’, semantic model arises as a solution of a domain equation involving the probabilistic powerdomain and solved in the category CONT⊥ of continuous domains. The second model also involves an appropriately restricted probabilistic powerdomain, but is constructed in the category CUM of complete ultra-metric spaces, and hence is necessarily ‘discrete’. We show that the domain-theoretic semantics is fully abstract with respect to the simulation preorder, and that the metric semantics is fully abstract with respect to bisimulation.
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HERNANDEZ, ENRIC, and JORDI RECASENS. "ON POSSIBILISTIC AND PROBABILISTIC APPROXIMATIONS OF UNRESTRICTED BELIEF FUNCTIONS BASED ON THE CONCEPT OF FUZZY T-PREORDER." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 02 (April 2002): 185–200. http://dx.doi.org/10.1142/s0218488502001417.

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This paper presents a new method for approximating an unrestricted belief measure assuring that the "order" defined by the compatibility degree between evidence and the singletons set is preserved. Our approach, based on the concept of fuzzy T-preorder, also allows us to define several equivalence criteria over the set of all basic probability assignment functions on a given domain. Some others related aspects as uniqueness of the approximations are also addressed.
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Cleaveland, Rance, Zeynep Dayar, Scott A. Smolka, and Shoji Yuen. "Testing Preorders for Probabilistic Processes." Information and Computation 154, no. 2 (November 1999): 93–148. http://dx.doi.org/10.1006/inco.1999.2808.

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Jonsson, Bengt, and Wang Yi. "Testing preorders for probabilistic processes can be characterized by simulations." Theoretical Computer Science 282, no. 1 (June 2002): 33–51. http://dx.doi.org/10.1016/s0304-3975(01)00044-5.

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Deng, Yuxin, and Alwen Tiu. "Characterisations of testing preorders for a finite probabilistic π-calculus." Formal Aspects of Computing 24, no. 4-6 (June 29, 2012): 701–26. http://dx.doi.org/10.1007/s00165-012-0238-3.

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Aguirre, Alejandro, and Lars Birkedal. "Step-Indexed Logical Relations for Countable Nondeterminism and Probabilistic Choice." Proceedings of the ACM on Programming Languages 7, POPL (January 9, 2023): 33–60. http://dx.doi.org/10.1145/3571195.

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Developing denotational models for higher-order languages that combine probabilistic and nondeterministic choice is known to be very challenging. In this paper, we propose an alternative approach based on operational techniques. We study a higher-order language combining parametric polymorphism, recursive types, discrete probabilistic choice and countable nondeterminism. We define probabilistic generalizations of may- and must-termination as the optimal and pessimal probabilities of termination. Then we define step-indexed logical relations and show that they are sound and complete with respect to the induced contextual preorders. For may-equivalence we use step-indexing over the natural numbers whereas for must-equivalence we index over the countable ordinals. We then show than the probabilities of may- and must-termination coincide with the maximal and minimal probabilities of termination under all schedulers. Finally we derive the equational theory induced by contextual equivalence and show that it validates the distributive combination of the algebraic theories for probabilistic and nondeterministic choice.
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Deng, Yuxin, Robert van Glabbeek, Matthew Hennessy, and Carroll Morgan. "Characterising Testing Preorders for Finite Probabilistic Processes." Logical Methods in Computer Science 4, no. 4 (October 28, 2008). http://dx.doi.org/10.2168/lmcs-4(4:4)2008.

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Wild, Paul, and Lutz Schröder. "Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions." Logical Methods in Computer Science Volume 18, Issue 2 (June 15, 2022). http://dx.doi.org/10.46298/lmcs-18(2:19)2022.

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In systems involving quantitative data, such as probabilistic, fuzzy, or metric systems, behavioural distances provide a more fine-grained comparison of states than two-valued notions of behavioural equivalence or behaviour inclusion. Like in the two-valued case, the wide variation found in system types creates a need for generic methods that apply to many system types at once. Approaches of this kind are emerging within the paradigm of universal coalgebra, based either on lifting pseudometrics along set functors or on lifting general real-valued (fuzzy) relations along functors by means of fuzzy lax extensions. An immediate benefit of the latter is that they allow bounding behavioural distance by means of fuzzy (bi-)simulations that need not themselves be hemi- or pseudometrics; this is analogous to classical simulations and bisimulations, which need not be preorders or equivalence relations, respectively. The known generic pseudometric liftings, specifically the generic Kantorovich and Wasserstein liftings, both can be extended to yield fuzzy lax extensions, using the fact that both are effectively given by a choice of quantitative modalities. Our central result then shows that in fact all fuzzy lax extensions are Kantorovich extensions for a suitable set of quantitative modalities, the so-called Moss modalities. For nonexpansive fuzzy lax extensions, this allows for the extraction of quantitative modal logics that characterize behavioural distance, i.e. satisfy a quantitative version of the Hennessy-Milner theorem; equivalently, we obtain expressiveness of a quantitative version of Moss' coalgebraic logic. All our results explicitly hold also for asymmetric distances (hemimetrics), i.e. notions of quantitative simulation.
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Dissertations / Theses on the topic "Probabilistic preorder"

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Sato, Tetsuya. "Identifying All Preorders on the Subdistribution Monad." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199080.

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PARMA, Augusto. "Axiomatic and logical characterizations of probabilistic preorders and trace semantics." Doctoral thesis, 2008. http://hdl.handle.net/11562/337598.

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Randomization was first introduced in computer science in order to improve the efficiency of several problems that were classified unfeasible or particularly inefficient, by giving algorithms the ability to flip coins, that is, of making probabilistic choices at some point of the computation. In the paper Probabilistic Algorithms, Rabin proposed efficient solutions to the problems of determining the nearest neighbor and to state the primality of a given number, for which there were no efficient non-probabilistic solutions. Later, he applied probability to a problem of distributed computing, which was not feasible without the use of randomiza- tion. On the base of these important results, a large set of problems were solved with the use of probabilistic choices in the computation, and a wide range of applications and modelings were proposed in the framework of concurrency theory. However, together with probabilistic behaviors, in the modeling and verification of concurrent processes it is crucial to take into account the presence of a phenomenon called nondeterminism. In general, nondeterminism is a way to model the lack of knowledge about the relative speeds of two or more processes running in parallel, as it may not be possible to determine which of the processes is performing the next action. On the other hand, there are further circumstances in which nondeterminism arises and must be modeled in order to obtain a correct description of the possible behaviors of a process. In particular, the external choices made by the environment in order to condition the execution of a process are modeled as nondeterministic choices, since the decisions taken by a user or by a malicious entity may not be predictable a priori by the system. Furthermore, since a semantic model of a process can be seen as a specification of the process, the introduction of nondeterministic choices in the model may reflect the ability to implement the specification by choosing one of the possible alternatives given, all leading to consistent implementations. The kinds of nondeterministic behaviors described can be all referred to as pure nondeterminism, in contrast with the probabilistic nondeterminism, which models the fact that events are governed by probability distributions.
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Book chapters on the topic "Probabilistic preorder"

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Cleaveland, Rance, Scott A. Smolka, and Amy Zwarico. "Testing preorders for probabilistic processes." In Automata, Languages and Programming, 708–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55719-9_116.

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Yuen, Shoji, Rance Cleaveland, Zeynep Dayar, and Scott A. Smolka. "Fully Abstract Characterizations of Testing Preorders for Probabilistic Processes." In CONCUR '94: Concurrency Theory, 497–512. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-540-48654-1_36.

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Höhle, Ulrich. "Many-Valued Preorders II: The Symmetry Axiom and Probabilistic Geometry." In Enric Trillas: A Passion for Fuzzy Sets, 151–65. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16235-5_11.

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Gaboardi, Marco, Shin-ya Katsumata, Dominic Orchard, and Tetsuya Sato. "Graded Hoare Logic and its Categorical Semantics." In Programming Languages and Systems, 234–63. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_9.

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AbstractDeductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by augmenting their rules with additional information to reason about program side-effects. For example, general program logics have been augmented with cost analyses, logics for probabilistic computations have been augmented with estimate measures, and logics for differential privacy with indistinguishability bounds. In this work, we unify these various approaches via the paradigm of grading, adapted from the world of functional calculi and semantics. We propose Graded Hoare Logic (GHL), a parameterisable framework for augmenting program logics with a preordered monoidal analysis. We develop a semantic framework for modelling GHL such that grading, logical assertions (pre- and post-conditions) and the underlying effectful semantics of an imperative language can be integrated together. Central to our framework is the notion of a graded category which we extend here, introducing graded Freyd categories which provide a semantics that can interpret many examples of augmented program logics from the literature. We leverage coherent fibrations to model the base assertion language, and thus the overall setting is also fibrational.
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Castagnoli, Erio, Marzia De Donno, Gino Favero, and Paola Modesti. "A Different Way to Look at Random Variables." In Analyzing Risk through Probabilistic Modeling in Operations Research, 179–99. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9458-3.ch008.

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A classical problem in Decision Theory is to represent a preference preorder among random variables. The fundamental Debreu's Theorem states that, in the discrete case, a preference satisfies the so-called Sure Thing Principle if and only if it can be represented by means of a function that can be additively decomposed along the states of the world where the random variables are defined. Such a representation suggests that every discrete random variable may be seen as a “histogram” (union of rectangles), i.e., a set. This approach leads to several fruitful consequences, both from a theoretical and an interpretative point of view. Moreover, an immediate link can be found with another alternative approach, according to which a decision maker sorts random variables depending on their probability of outperforming a given benchmark. This way, a unified approach for different points of view may be achieved.
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Conference papers on the topic "Probabilistic preorder"

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Deng, Yuxin, Rob van Glabbeek, Matthew Hennessy, Carroll Morgan, and Chenyi Zhang. "Characterising Testing Preorders for Finite Probabilistic Processes." In 2007 22nd Annual IEEE Symposium on Logic in Computer Science. IEEE, 2007. http://dx.doi.org/10.1109/lics.2007.15.

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