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Axiomatizing Bisimulation Equivalences and Metrics from Probabilistic SOS Rules [chapter]

Pedro R. D'Argenio, Daniel Gebler, Matias David Lee
2014 Lecture Notes in Computer Science  
Bisimulation equivalences and bisimulation metrics are fundamental notions to describe behavioral relations and distances of states, respectively.  ...  Furthermore, we generalize this method to axiomatize the strong and convex metric bisimulation distance of PTSS.  ...  Equality follows from the fact that d is the smallest bisimulation metric.  ... 
doi:10.1007/978-3-642-54830-7_19 fatcat:dg53fmunxfc6hlomlm7pbk7e7q

Continuous Markovian Logic - From Complete Axiomatization to the Metric Space of Formulas

Luca Cardelli, Kim G. Larsen, Radu Mardare, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
In this paper we present a sound and complete Hilbert-style axiomatization of CML for the CMP-semantics and prove some metaproperties including the small model property.  ...  CML characterizes stochastic bisimulation and supports the definition of a quantified extension of satisfiability relation that measures the compatibility of a model and a property.  ...  Section 6 introduces the metric semantics and the results related to metrics and bisimulation.  ... 
doi:10.4230/lipics.csl.2011.144 dblp:conf/csl/CardelliLM11 fatcat:yi2pch3n6faptpaazb6iqjob5a

Fourth International Conference on the Quantitative Evaluation of Systems-Title

2007 Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)  
Especially the definition of weak (symbolic) bisimulation does not rely on the random capability of adversaries and suggests a solution to the open problem on the axiomatization for weak bisimulation in  ...  Furthermore, we present an efficient characterization of symbolic bisimulations for the calculus, which allows the "on-the-fly" instantiation of bound names and dynamic construction of equivalence relations  ...  Acknowledgements The work of Peng Wu and Catuscia Palamidessi was partially supported by the INRIA/ARC project ProNoBis.  ... 
doi:10.1109/qest.2007.46 fatcat:4ukmmww4yfcj5jwqyacrdzrlau

Symbolic Bisimulations for Probabilistic Systems

Peng Wu, Catuscia Palamidessi, Huimin Lin
2007 Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)  
Especially the definition of weak (symbolic) bisimulation does not rely on the random capability of adversaries and suggests a solution to the open problem on the axiomatization for weak bisimulation in  ...  Furthermore, we present an efficient characterization of symbolic bisimulations for the calculus, which allows the "on-the-fly" instantiation of bound names and dynamic construction of equivalence relations  ...  Valuable comments and suggestions from anonymous referees are also appreciated.  ... 
doi:10.1109/qest.2007.11 dblp:conf/qest/WuPL07 fatcat:jfk4uwcqvbf4toro3fgmeascna

Parameterized Metatheory for Continuous Markovian Logic

Kim G. Larsen, Radu Mardare, Claus Thrane
2012 Electronic Proceedings in Theoretical Computer Science  
by a sound and complete axiomatization and prove a series of "parameterized" metatheorems including decidability, weak completeness and finite model property.  ...  Using this framework, we can characterize both the stochastic bisimulation relation and various observational preorders based on behavioural pseudometrics.  ...  Acknowledgement This research was supported by the VKR Center of Excellence MT-LAB and by the Sino-Danish Basic Research Center IDEA4CPS.  ... 
doi:10.4204/eptcs.103.4 fatcat:opq3irglgffs3oak4sxe4talma

The Measurable Space of Stochastic Processes

Luca Cardelli, Radu Mardare
2010 2010 Seventh International Conference on the Quantitative Evaluation of Systems  
We prove that stochastic bisimulation is a congruence that extends structural congruence.  ...  The measures encode the rates of the transitions from a process (state of a system) to a measurable set of processes.  ...  the probabilistic bisimulation of [24] , is defined and studied.  ... 
doi:10.1109/qest.2010.30 dblp:conf/qest/CardelliM10 fatcat:rnxsy2igdvfdbjqwpyq3anlqhi

Continuous Markovian Logics - Axiomatization and Quantified Metatheory

Radu Mardare, Luca Cardelli, Kim Larsen, Marc Bezem
2012 Logical Methods in Computer Science  
In this paper we present weak and strong complete axiomatizations for CML and prove a series of metaproperties, including the finite model property and the construction of canonical models.  ...  CML characterizes stochastic bisimilarity and it supports the definition of a quantified extension of the satisfiability relation that measures the "compatibility" between a model and a property.  ...  Mardare would like to thank to Prakash Panangaden, Dexter Kozen, Chunlai Zhou and Ernst-Erich Doberkat for discussions regarding various aspects of the theory of Markov processes and logics that eventually  ... 
doi:10.2168/lmcs-8(4:19)2012 fatcat:i5medzrdtjekrancdvs3kpkyga

Complete Axiomatization for the Total Variation Distance of Markov Chains

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare
2018 Electronical Notes in Theoretical Computer Science  
In this paper, we present a sound and complete axiomatization for the total variation distance on labelled Markov chains, i.e. a natural metric-lifting of probabilistic trace equivalence.  ...  Markov chains and greatly developed and explored by van Breugel, Worrell and others Recently, in [4], we provided a sound and complete axiomatization for the probabilistic bisimilarity distance of Desharnais  ...  Acknowledgment We would like to thank Frank van Breugel for suggesting the topic this paper, and Ana Sokolova and Alexandra Silva for pointing out some issues on a preliminary version of this paper.  ... 
doi:10.1016/j.entcs.2018.03.014 fatcat:5ateotofovgatpjzakwccrcn6m

A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains [article]

Giorgio Bacci and Giovanni Bacci and Kim G. Larsen and Radu Mardare
2018 arXiv   pre-print
Notably, our quantitative deduction system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich  ...  The axiomatization is then used to propose a metric extension of a Kleene's style representation theorem for finite labelled Markov chains, that was proposed (in a more general coalgebraic fashion) by  ...  One of them, namely the axiomatization of the discounted probabilistic bisimilarity distance, has been developed in this extended version; the others have been resolved in [BBLM18] .  ... 
arXiv:1702.02528v4 fatcat:orvy7pntmzgt7ce573hzag2vfq

Upper-Expectation Bisimilarity and Real-valued Modal Logics [article]

Matteo Mio
2013 arXiv   pre-print
We consider a novel testing-based behavioral equivalence called upper-expectation bisimilarity and develop its theory using standard results from linear algebra and functional analysis.  ...  Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature.  ...  Hence the metric d ′ (A, B) = g:X→[0,1] |ue A (g) − ue B (g)| is equivalent to d mH (A, B), i.e., the two metrics induce the same topology.  ... 
arXiv:1310.0768v1 fatcat:7gvzvew36nd6neh6p6hlp6w3pe

Probabilistic systems coalgebraically: A survey

Ana Sokolova
2011 Theoretical Computer Science  
and behavioral equivalence, mentioning results that follow from the coalgebraic treatment of probabilistic systems.  ...  It is interesting to note that, for different reasons, for both discrete and continuous probabilistic systems it may be more convenient to work with behavioral equivalence than with bisimilarity.  ...  Furthermore, I would like to thank Dirk Pattinson for discussions and pointers to references, Lutz Schröder for a comment during my talk at CMCS 2010, a prompt answer to a question, and just-in-time pointers  ... 
doi:10.1016/j.tcs.2011.05.008 pmid:21998490 pmcid:PMC3185909 fatcat:z4iljxlfofc5jbzyg3bwxk4g5y

A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
that modal logic is precisely the bisimulation-invariant fragment of first-order logic.  ...  The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance.  ...  Given models I, J , a 0 ∈ ∆ I , b 0 ∈ ∆ J , and 0 ∈ [0, 1], the 0 -bisimulation game for a 0 and b 0 is played by Spoiler (S) and Duplicator (D), with rules as follows: • Configurations: triples (a, b  ... 
doi:10.24963/ijcai.2019/263 dblp:conf/ijcai/WildSP019 fatcat:b74qeyfflzchbjgynfhkyca62y

Modular Markovian Logic [chapter]

Luca Cardelli, Kim G. Larsen, Radu Mardare
2011 Lecture Notes in Computer Science  
We present a complete Hilbert-style axiomatization for MML, prove the small model property and analyze the relation between the stochastic bisimulation and the logical equivalence relation induced by MML  ...  Given two measurable spaces (M, Σ) and (N, Θ) , a mapping f : M → N is measurable if for any T ∈ Θ, f −1 (T ) ∈ Σ. We use M → N to denote the class of measurable mappings from (M, Σ) to (N, Θ).  ...  Section 3 defines MMPs and their bisimulation. Section 4 presents MML and results concerning the relationship between logical equivalence and bisimulation.  ... 
doi:10.1007/978-3-642-22012-8_30 fatcat:ze5n3qentrdmzjp3auwpbcczgi

Upper-Expectation Bisimilarity and Łukasiewicz μ-Calculus [chapter]

Matteo Mio
2014 Lecture Notes in Computer Science  
We study a novel testing-based behavioral equivalence called upper expectation bisimilarity and, using standard results from functional analysis, we develop its coalgebraic and algebraic theory and provide  ...  Several notions of bisimulation relations for probabilistic nondeterministic transition systems have been considered in the literature.  ...  Upper-Expectation Bisimilarity and Lukasiewicz μ-Calculus  ... 
doi:10.1007/978-3-642-54830-7_22 fatcat:zqn7qfnehrerflmrlivlestnra

Structural Operational Semantics

Luca Aceto, Willem Jan Fokkink, Chris Verhoef
1999 BRICS Report Series  
advocated by McCarthy<br />in [147], and elaborated upon in references like [142, 143].  ...  Examples of full-blown<br />languages that have been endowed with an operational semantics are<br />Algol 60 [140], PL/I [173], and CSP [178].  ...  Bergstra and Klop presented in op. cit. an axiomatization E 0 that is complete over BPA δ modulo bisimulation equivalence, and an axiomatization E 0 ∪ E 1 that is sound over ACP modulo bisimulation equivalence  ... 
doi:10.7146/brics.v6i30.20099 fatcat:vfrxsl34ijgplci55tscmz2aue
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