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Journal articles on the topic 'Approximate bisimulation'

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Author: Grafiati

Published: 11 March 2023

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1

Ma, Yanfang. "Quantitative Analysis of Software Approximate Correctness." Mathematical Problems in Engineering 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/173012.

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Parameterized bisimulation provides an abstract description of software correctness. In real world situations, however, many software products are approximately correct. To characterize the approximate correctness, we generalize the parameterized bisimulation to numerical version and probabilistic setting. First, we propose the definition of the parameterized bisimulation index that expresses the degree to which a binary relation is parameterized bisimulation. Then,λ-parameterized bisimulation over environmenteand its substitutivity laws are presented. Finally,λ-parameterized probabilistic bisimulation is established to describe complicated software products with probabilistic phenomena.

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2

Deng, Hui, and Jinzhao Wu. "Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation." Mathematical Problems in Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/421926.

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To achieve behavior and structure optimization for a type of software program whose data exchange processes are represented by nonlinear polynomial systems, this paper establishes a novel formal description called a nonlinear polynomial transition system to represent the behavior and structure of the software program. Then, the notion of bisimulation for software programs is proposed based on the equivalence relation of corresponding nonlinear polynomial systems in their nonlinear polynomial transition systems. However, the exact equivalence is too strict in application. To enhance the flexibility of the relation among the different software systems, the notion of approximate bisimulation within a controllable error range and the calculation algorithm of approximate bisimulation based on symbolic-numeric computation are given. In this calculation, an approximate relation is represented as a MAX function that is resolved with the full filled method. At the same time, the actual error is calculable. An example on a multithreading program indicates that the approximate bisimulation relation is feasible and effective in behavior and structure optimization.

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3

Yang, Chao, and Yongming Li. "Approximate bisimulation relations for fuzzy automata." Soft Computing 22, no. 14 (November 9, 2017): 4535–47. http://dx.doi.org/10.1007/s00500-017-2913-z.

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4

Liu, Bai, Jinzhao Wu, and Zhucheng Xie. "Approximate Bisimulation Equivalence and Variable Refinement." Applied Mathematics & Information Sciences 8, no. 4 (July 1, 2014): 1959–66. http://dx.doi.org/10.12785/amis/080454.

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5

Gebler, Daniel, and Simone Tini. "Compositionality of Approximate Bisimulation for Probabilistic Systems." Electronic Proceedings in Theoretical Computer Science 120 (July 26, 2013): 32–46. http://dx.doi.org/10.4204/eptcs.120.4.

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6

Girard, Antoine, and George J. Pappas. "Approximate bisimulation relations for constrained linear systems." Automatica 43, no. 8 (August 2007): 1307–17. http://dx.doi.org/10.1016/j.automatica.2007.01.019.

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7

Girard, Antoine. "Low-complexity quantized switching controllers using approximate bisimulation." Nonlinear Analysis: Hybrid Systems 10 (November 2013): 34–44. http://dx.doi.org/10.1016/j.nahs.2013.02.001.

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8

Wang, Chao, Jinzhao Wu, Hongyan Tan, and Jun Fu. "Approximate reachability and bisimulation equivalences for transition systems." Transactions of Tianjin University 22, no. 1 (February 2016): 19–23. http://dx.doi.org/10.1007/s12209-016-2565-6.

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9

CHOE, Sunseong, Kunihiko HIRAISHI, and Koichi KOBAYASHI. "Approximate Bisimulation for Hybrid Systems Based on Transition Relations." Transactions of the Society of Instrument and Control Engineers 47, no. 12 (2011): 614–20. http://dx.doi.org/10.9746/sicetr.47.614.

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10

Stankovic, Aleksandar M., Savo D. Dukic, and Andrija T. Saric. "Approximate Bisimulation-Based Reduction of Power System Dynamic Models." IEEE Transactions on Power Systems 30, no. 3 (May 2015): 1252–60. http://dx.doi.org/10.1109/tpwrs.2014.2342504.

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11

Ma, Yanfang, and Haiyu Pan. "The Approximate Correctness of Systems Based on δ -bisimulation." Electronic Notes in Theoretical Computer Science 333 (September 2017): 73–87. http://dx.doi.org/10.1016/j.entcs.2017.08.007.

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12

Girard, Antoine. "Controller synthesis for safety and reachability via approximate bisimulation." Automatica 48, no. 5 (May 2012): 947–53. http://dx.doi.org/10.1016/j.automatica.2012.02.037.

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13

Girard, Antoine, and George J. Pappas. "Approximate Bisimulation: A Bridge Between Computer Science and Control Theory." European Journal of Control 17, no. 5-6 (January 2011): 568–78. http://dx.doi.org/10.3166/ejc.17.568-578.

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14

Deng, Hui, Jinzhao Wu, and Hongyan Tan. "Approximate Bisimulation for High-Level Datapaths in Intelligent Transportation Systems." Advances in Mechanical Engineering 5 (January 2013): 305636. http://dx.doi.org/10.1155/2013/305636.

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15

Ariful Islam, Md, Abhishek Murthy, Ezio Bartocci, Elizabeth M. Cherry, Flavio H. Fenton, James Glimm, Scott A. Smolka, and Radu Grosu. "Model-order reduction of ion channel dynamics using approximate bisimulation." Theoretical Computer Science 599 (September 2015): 34–46. http://dx.doi.org/10.1016/j.tcs.2014.03.018.

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16

Pola, Giordano, Pierdomenico Pepe, and Maria Domenica Di Benedetto. "Symbolic models for time-varying time-delay systems via alternating approximate bisimulation." International Journal of Robust and Nonlinear Control 25, no. 14 (June 27, 2014): 2328–47. http://dx.doi.org/10.1002/rnc.3204.

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17

Qiao, Sha, and Ping Zhu. "Limited approximate bisimulations and the corresponding rough approximations." International Journal of Approximate Reasoning 130 (March 2021): 50–82. http://dx.doi.org/10.1016/j.ijar.2020.12.005.

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18

Pola, Giordano, and Paulo Tabuada. "Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations." SIAM Journal on Control and Optimization 48, no. 2 (January 2009): 719–33. http://dx.doi.org/10.1137/070698580.

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19

Pola, Giordano, Pierdomenico Pepe, Maria D. Di Benedetto, and Paulo Tabuada. "Symbolic models for nonlinear time-delay systems using approximate bisimulations." Systems & Control Letters 59, no. 6 (June 2010): 365–73. http://dx.doi.org/10.1016/j.sysconle.2010.04.001.

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20

Delgrange, Florent, Ann Nowé, and Guillermo A. Pérez. "Distillation of RL Policies with Formal Guarantees via Variational Abstraction of Markov Decision Processes." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (June 28, 2022): 6497–505. http://dx.doi.org/10.1609/aaai.v36i6.20602.

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We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in the limit. While these guarantees are valuable, they are insufficient for safety-critical applications. Furthermore, they are lost when applying advanced techniques such as deep-RL. To recover guarantees when applying advanced RL algorithms to more complex environments with (i) reachability, (ii) safety-constrained reachability, or (iii) discounted-reward objectives, we build upon the DeepMDP framework to derive new bisimulation bounds between the unknown environment and a learned discrete latent model of it. Our bisimulation bounds enable the application of formal methods for Markov decision processes. Finally, we show how one can use a policy obtained via state-of-the-art RL to efficiently train a variational autoencoder that yields a discrete latent model with provably approximately correct bisimulation guarantees. Additionally, we obtain a distilled version of the policy for the latent model.

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21

Yang, Chao, and Yongming Li. "Approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures." Fuzzy Sets and Systems 391 (July 2020): 72–95. http://dx.doi.org/10.1016/j.fss.2019.07.010.

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22

HONSELL, FURIO, and MARINA LENISA. "Coinductive characterizations of applicative structures." Mathematical Structures in Computer Science 9, no. 4 (August 1999): 403–35. http://dx.doi.org/10.1017/s096012959900287x.

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We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on λ-terms and, more generally, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss, in particular, what we call the cartesian coinduction principle, which arises when we exploit the elementary observation that functional behaviours can be expressed as cartesian graphs. Using the paradigm of final semantics, the soundness of this principle over an applicative structure can be expressed easily by saying that the applicative structure can be construed as a strongly extensional coalgebra for the functor ([Pscr ](- × -))[oplus ]([Pscr ](- × -)). In this paper we present two general methods for showing the soundness of this principle. The first applies to approximable applicative structures – many CPO λ-models in the literature and the corresponding quotient models of indexed terms turn out to be approximable applicative structures. The second method is based on Howe's congruence candidates, which applies to many observational equivalences. Structures satisfying cartesian coinduction are precisely those applicative structures that can be modelled using the standard set-theoretic application in non-wellfounded theories of sets, where the Foundation Axiom is replaced by the Axiom X1 of Forti and Honsell.

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23

Ruan, Sherry, Gheorghe Comanici, Prakash Panangaden, and Doina Precup. "Representation Discovery for MDPs Using Bisimulation Metrics." Proceedings of the AAAI Conference on Artificial Intelligence 29, no. 1 (March 4, 2015). http://dx.doi.org/10.1609/aaai.v29i1.9747.

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We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs.We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.

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24

Ruan, Sherry, Gheorghe Comanici, Prakash Panangaden, and Doina Precup. "Representation Discovery for MDPs Using Bisimulation Metrics." Proceedings of the AAAI Conference on Artificial Intelligence 29, no. 1 (March 4, 2015). http://dx.doi.org/10.1609/aaai.v29i1.9701.

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We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs. We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.

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25

Wang, Fujun, Zining Cao, Lixing Tan, and Zhen Li. "Formal Modeling and Performance Evaluation for Hybrid Systems: A Probabilistic Hybrid Process Algebra-Based Approach." International Journal of Software Engineering and Knowledge Engineering, April 4, 2022, 1–33. http://dx.doi.org/10.1142/s0218194022500103.

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Probabilistic behavior is omnipresent in computer-controlled systems, in particular, so-called safety-critical hybrid systems, due to various reasons, like uncertain environments or fundamental properties of nature. In this paper, we extend the existing hybrid process algebra ACP[Formula: see text] with probability without sacrificing the nondeterministic choice operator. The existing approximate probabilistic bisimulation relation is fragile and not robust in the sense of being dependent on the deviation range of the transition probability. To overcome this defect, a novel approximate probabilistic bisimulation is proposed which is inspired by the idea of Probably Approximately Correct (PAC) by relaxing the constraints of transition probability deviation range. Traditional temporal logics, even probabilistic temporal logics, are expressive enough, but they are limited to producing only true or false responses, as they are still logics and not suitable for performance evaluation. To settle this problem, we present a new performance evaluation language that expands quantitative analysis from the value range of [Formula: see text] to real number to reason over probabilistic systems. After that, the corresponding algorithms for performance evaluation are given. Finally, an industrial example is given to demonstrate the effectiveness of our method.

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26

Sprunger, David, Shin-ya Katsumata, Jérémy Dubut, and Ichiro Hasuo. "Fibrational bisimulations and quantitative reasoning: Extended version." Journal of Logic and Computation, September 10, 2021. http://dx.doi.org/10.1093/logcom/exab051.

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Abstract Bisimulation and bisimilarity are fundamental notions in comparing state-based systems. Their extensions to a variety of systems have been actively pursued in recent years, a notable direction being quantitative extensions. In this paper we enhance a categorical framework for such extended (bi)simulation notions. We use coalgebras as system models and fibrations for organizing predicates—following the seminal work by Hermida and Jacobs. Endofunctor liftings are crucial predicate-forming ingredients; the first contribution of this work is to extend several extant lifting techniques from particular fibrations to $\textbf {CLat}_\wedge $-fibrations over $\textbf {Set}$. The second contribution of this work is to introduce endolifting morphisms as a mechanism for comparing predicates between fibrations. We apply these techniques by deriving some known properties of the Hausdorff pseudometric and approximate bisimulation in control theory.

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27

Micić, Ivana, Linh Anh Nguyen, and Stefan Stanimirović. "Characterization and computation of approximate bisimulations for fuzzy automata." Fuzzy Sets and Systems, May 2022. http://dx.doi.org/10.1016/j.fss.2022.05.003.

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28

Stanimirovic, Stefan, Ivana Micic, and Miroslav Ciric. "Approximate Bisimulations for Fuzzy Automata over Complete Heyting Algebras." IEEE Transactions on Fuzzy Systems, 2020, 1. http://dx.doi.org/10.1109/tfuzz.2020.3039968.

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