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SOS-based Modal Decomposition on Nondeterministic Probabilistic Processes [article]

Valentina Castiglioni, Daniel Gebler, Simone Tini
2017 arXiv   pre-print
We propose a method for the decomposition of modal formulae on processes with nondeterminism and probability with respect to Structural Operational Semantics.  ...  To deal with the probabilistic behavior of processes, and thus with the decomposition of formulae characterizing it, we introduce a SOS-like machinery allowing for the specification of the behavior of  ...  Conclusions We developed a modal decomposition of formulae in L and its subclasses L r , L + , on nondeterministic probabilistic processes.  ... 
arXiv:1701.08330v2 fatcat:5xxg33wzjvazdfk2tkyhoqstjq

Compositionality of Probabilistic Hennessy-Milner Logic through Structural Operational Semantics [chapter]

Daniel Gebler, Wan Fokkink
2012 Lecture Notes in Computer Science  
This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras.  ...  We present a method to decompose HML formulae for reactive probabilistic processes.  ...  Acknowledgements We are grateful to Simone Tini for discussions on structural properties of operational semantics for PLTSs, and to Bas Luttik for constructive feedback on the presentation of the research  ... 
doi:10.1007/978-3-642-32940-1_28 fatcat:iu6kqak2pnbh7dbiwnyymt4vlm

Logical Characterization of Bisimulation Metrics

Valentina Castiglioni, Daniel Gebler, Simone Tini
2016 Electronic Proceedings in Theoretical Computer Science  
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes.  ...  In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic.  ...  The modal logic L We introduce the modal logic L of [19] , which extends HML [41] with a probabilistic choice modality that allows us to express the behavior of probabilistic distributions over processes  ... 
doi:10.4204/eptcs.227.4 fatcat:k4h6kolaprgg3lfx724s4gbhzm

Book Introduction by the Author: Semantics of Probabilistic Processes An Operational Approach

Yuxin Deng
2015 Bulletin of the European Association for Theoretical Computer Science  
In "Semantics of Probabilistic Processes" [4] we adopt an operational approach to describing the behaviour of nondeterministic and probabilistic processes.  ...  The second part sets up a general testing framework and specialises it to probabilistic processes with nondeterministic behaviour. The resulting testing semantics is treated in depth.  ...  My research on probabilistic concurrency theory has been sponsored by the National Natural Science Foundation of China under grants 61173033 and 61261130589.  ... 
dblp:journals/eatcs/Deng15 fatcat:wardvn6yr5ah3ahdxmmlhvypu4

Characterising Probabilistic Processes Logically [chapter]

Yuxin Deng, Rob van Glabbeek
2010 Lecture Notes in Computer Science  
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour.  ...  We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence.  ...  The first papers on probabilistic concurrency theory [11, 2, 19] proceed by replacing nondeterministic with probabilistic constructs.  ... 
doi:10.1007/978-3-642-16242-8_20 fatcat:kouw2nzjmrdj5iqzo3okby3vvy

Quantitative Program Logic and Performance in Probabilistic Distributed Algorithms [chapter]

Annabelle K. McIver
1999 Lecture Notes in Computer Science  
We illustrate the methods with an analysis of performance of the probabilistic dining philosophers [10] .  ...  quantitative program logic [14] provides a formal framework in which to promote standard techniques of program analysis to a context where probability and nondeterminism interact, a situation common to probabilistic  ...  Deciding how to choose an appropriate decomposition often depends on the probabilistic invariant properties, and we discuss them next.  ... 
doi:10.1007/3-540-48778-6_2 fatcat:oblrgrjcbndebasdxy4nlmi6fe

A Local Algorithm for Checking Probabilistic Bisimilarity

Yuxin Deng, Wenjie Du
2009 2009 Fourth International Conference on Frontier of Computer Science and Technology  
Bisimilarity is one of the most important relations for comparing the behaviour of formal systems in concurrency theory.  ...  In this paper we propose a polynomial time local algorithm for checking probabilistic bisimilarity.  ...  The first papers on probabilistic concurrency theory [23] , [8] , [32] proceed by replacing nondeterministic with probabilistic constructs.  ... 
doi:10.1109/fcst.2009.37 dblp:conf/fcst/DengD09 fatcat:gppw2no62nf6dbe45mojtamcwe

Modal Logics are Coalgebraic

C. Cirstea, A. Kurz, D. Pattinson, L. Schroder, Y. Venema
2009 Computer journal  
This paper substantiates the authors' firm belief that the systematic exploitation of this coalgebraic nature will not only have impact on the field of modal logic itself but also lead to significant progress  ...  Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains.  ...  for Segala systems advocated in [24] that distinguishes probabilistic and nondeterministic formulas.  ... 
doi:10.1093/comjnl/bxp004 fatcat:gpm47rtxanb5xaei7nq3z4pnea

Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation [article]

Yuxin Deng, Wenjie Du
2011 arXiv   pre-print
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states.  ...  Specifically, we extend the Hennessy-Milner logic and the modal mu-calculus with a new modality, resulting in an adequate and an expressive logic for probabilistic bisimilarity, respectively.  ...  In the belief that a good scientific concept is often elegant, even seen from different perspectives, we consider the lifting operation and probabilistic bisimulation as two concepts in probabilistic concurrency  ... 
arXiv:1103.4577v1 fatcat:z626tecr4ndqdokqr3cvosn2gm

Modal Characterisations of Probabilistic and Fuzzy Bisimulations [chapter]

Yuxin Deng, Hengyang Wu
2014 Lecture Notes in Computer Science  
Furthermore, inspired by the work of Hermanns et al. on probabilistic systems, we provide a sound and complete modal characterisation of fuzzy bisimilarity.  ...  generalises a result on finite-state processes originally established by Baier; (2) the modal characterisation of bisimilarity by Desharnais et al. admits a much simpler completeness proof.  ...  Acknowledgement We thank the anonymous referees for their helpful comments on a preliminary version of the paper.  ... 
doi:10.1007/978-3-319-11737-9_9 fatcat:cenbl22w6jdpjpxoshwvpudegu

"Quantal" behavior in classical probability [article]

K. A. Kirkpatrick
2003 arXiv   pre-print
Value-indeterminacy is a normal possibility in a nondeterministic system (at a certain point in the manifestation process, a nondeterministic choice brings one variable's value into existence, and, at  ...  which causes a variable P to take on one of its values; I call that process the manifestation of P and denote it M P .  ...  (No exercise regarding Q3 is possible: because observations on this system do not repeat, "sharpness" has no meaning.)  ... 
arXiv:quant-ph/0106072v6 fatcat:kd6warxul5cvvcxffig5tetx24

Quantitative program logic and expected time bounds in probabilistic distributed algorithms

A.K. McIver
2002 Theoretical Computer Science  
We illustrate the methods with an analysis of expected running time of the probabilistic dining philosophers (Lehmann and Ravin,  ...  Languages Systems 18 (1996) 325) provides a formal framework in which to promote standard techniques of program analysis to a context where probability and nondeterminism interact, a situation common to probabilistic  ...  the 'for all' modality of transition semantics [1] .  ... 
doi:10.1016/s0304-3975(01)00049-4 fatcat:mncofranmbgvjksnmifadv3csa

Dynamic Logics of Dynamical Systems [article]

André Platzer
2012 arXiv   pre-print
A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior.  ...  In this survey, we focus on some of the representatives of the family of differential dynamic logics, which share the ability to express properties of dynamical systems having continuous dynamics described  ...  My thanks go to Sicun Gao, David Harel, David Henriques, Oded Maler, João Martins, Sayan Mitra, Vaughan Pratt, and Sriram Sankaranarayanan for feedback on this article.  ... 
arXiv:1205.4788v1 fatcat:2ahunsfdzfamdiwzd66m5e4wzq

Bialgebraic Methods in Structural Operational Semantics

Bartek Klin
2007 Electronical Notes in Theoretical Computer Science  
In particular, a combination of basic bialgebraic techniques with a categorical approach to modal logic is described, as an abstract approach to proving compositionality by decomposing modal logics over  ...  Modal logic decomposition In a coalgebraic approach to modal logics and system testing [15, 26, 34] , one considers a contravariant adjunction between a category C of processes, where coalgebras for a  ...  Examples include probabilistic, timed and hybrid systems, ones with global or local state, name passing, process passing, and stochastic systems.  ... 
doi:10.1016/j.entcs.2006.11.018 fatcat:ulqmznw4vvctrbah5pfu7wj6gi

Behavioural Pseudometrics for Nondeterministic Probabilistic Systems [chapter]

Wenjie Du, Yuxin Deng, Daniel Gebler
2016 Lecture Notes in Computer Science  
We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic.  ...  For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the  ...  Metrics for nondeterministic probabilistic systems are considered in [17] , where Desharnais et al. deal with labelled concurrent Markov chains (similar to pLTSs, this model can be captured by the simple  ... 
doi:10.1007/978-3-319-47677-3_5 fatcat:7tcqhmhlvzcuph5bp6wgidqage
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