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Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems

Franck van Breugel, Babita Sharma, James Worrell, Helmut Seidl
2008 Logical Methods in Computer Science  
Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems.  ...  These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity.  ...  Acknowledgement The authors would like to thank Christel Baier for providing some pointers to the literature and Jeff Edmonds, Parke Godfrey and the referees for their constructive feedback.  ... 
doi:10.2168/lmcs-4(2:2)2008 fatcat:e7ancy7e2zhophy7a5mt6yuufe

Approximating a Behavioural Pseudometric Without Discount for Probabilistic Systems [chapter]

Franck van Breugel, Babita Sharma, James Worrell
2007 Lecture Notes in Computer Science  
Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems.  ...  These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity.  ...  Acknowledgements The authors would like to thank Christel Baier for providing some pointers to the literature.  ... 
doi:10.1007/978-3-540-71389-0_10 fatcat:o73ot4ej6rffbbznhkz6pjnsre

Recursively defined metric spaces without contraction

Franck van Breugel, Claudio Hermida, Michael Makkai, James Worrell
2007 Theoretical Computer Science  
For instance, using the Kantorovich metric on probability measures we construct a quantitative model for probabilistic transition systems.  ...  The metric in our model can reasonably be seen as measuring the behavioural distance between states of the system; it depends exclusively on the transition probabilities and not on an arbitrary discount  ...  Acknowledgements The authors thank Jiří Adámek, Michael Barr and the referees for their helpful comments.  ... 
doi:10.1016/j.tcs.2007.02.059 fatcat:6vv5kwjt2nf2baaldejzbnqfi4

Approximating and computing behavioural distances in probabilistic transition systems

Franck van Breugel, James Worrell
2006 Theoretical Computer Science  
In an earlier paper we presented a pseudometric on the states of a probabilistic transition system, yielding a quantitative notion of behavioural equivalence.  ...  The behavioural pseudometric was defined via the terminal coalgebra of a functor based on a metric on Borel probability measures.  ...  Acknowledgements We would like to thank the referees for their constructive feedback.  ... 
doi:10.1016/j.tcs.2006.05.021 fatcat:ase767krqvbdnnd7azkqi3mi2y

A Framework for Supervisory Control of Probabilistic Discrete Event Systems

Vera Pantelic, Mark Lawford, Steven Postma
2014 IFAC Proceedings Volumes  
This paper focuses on a framework for probabilistic supervisory control of probabilistic discrete event systems (PDES).  ...  We also suggested a pseudometric to measure the behavioural similarity between PDES, and used the pseudometric in the solution of two optimal supervisory control problems defined in the framework.  ...  Measuring Similarity Between PDES Behavioural similarity between the systems in our framework is measured using a pseudometric 1 .  ... 
doi:10.3182/20140514-3-fr-4046.00073 fatcat:lzmqsrv4iraepcyn2l4phkvrf4

Towards Optimal Supervisory Control of Probabilistic Discrete Event Systems

Vera Pantelic, Mark Lawford
2009 IFAC Proceedings Volumes  
Then, given a plant and a desired probabilistic behaviour, we present an algorithm that minimizes the distance between the desired behaviour and the behaviour of the controlled plant achievable under probabilistic  ...  We consider the case when there exists no probabilistic supervisor to match the behaviour of a plant to a probabilistic requirements specification.  ...  As a more flexible way to compare probabilistic systems, a notion of pseudometric is introduced.  ... 
doi:10.3182/20090610-3-it-4004.00018 fatcat:7txtylch7zfpvcxof4iqk5ovpa

A behavioural pseudometric for probabilistic transition systems

Franck van Breugel, James Worrell
2005 Theoretical Computer Science  
In this paper, we present a pseudometric on a class of probabilistic transition systems yielding a quantitative notion of behavioural equivalence.  ...  Discrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems.  ...  Furthermore, the authors are grateful to the referees for their comments. The first author is thankful to Stephen Watson for the joint study of metrics on probability measures.  ... 
doi:10.1016/j.tcs.2004.09.035 fatcat:t3wwa33yjjgibcb5g5tr3sxt5q

Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, Franck Van Breugel, Michael Wagner
2019 International Conference on Concurrency Theory  
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata.  ...  In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game.  ...  A behavioural pseudometric for probabilistic automata capturing this difference is the probabilistic bisimilarity distance by Deng et al.  ... 
doi:10.4230/lipics.concur.2019.9 dblp:conf/concur/BacciBLMTB19 fatcat:qjnelkx5czexvnbk5ntoutbnsq

A van Benthem Theorem for Quantitative Probabilistic Modal Logic [article]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2019 arXiv   pre-print
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity.  ...  For probabilistic systems, probabilistic modal logic thus plays an analogous role to that of Hennessy-Milner logic on classical labelled transition systems.  ...  We have already mentioned work on behavioural distance in probabilistic systems [17, 10, 42, 12, 2, 6] ; concretely, the Kantorovich-style discount-free notion of behavioural distance that we use here  ... 
arXiv:1810.04722v2 fatcat:wu4kpdw4d5btzmi2hiwz72fdqu

Polynomial-time algorithms for computing distances of fuzzy transition systems

Taolue Chen, Tingting Han, Yongzhi Cao
2018 Theoretical Computer Science  
In other words, discounting models preference for shorter solutions. We introduce discounting into the distance definition for fuzzy transition systems, as done in probabilistic systems [28] .  ...  For probabilistic systems, different algorithms have been provided for a variety of stochastic models (cf. the related work).  ...  Given any FTS f ||, which follows from Lemma 6 and the fact that γ (d for some aA, μ ∈ δ(s, a), and η ∈ δ(t, a). Namely d(s, t) = γ · u,v∈S (d(u, v)  ... 
doi:10.1016/j.tcs.2018.03.002 fatcat:b37jpiykpbbcjb446g6xppgrki

Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions

Paul Wild, Lutz Schröder
2022 Logical Methods in Computer Science  
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  ...  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.  ...  Like their two-valued counterparts, behavioural distances have been introduced for quite a range of system types, such as various forms of probabilistic labelled transition systems or labelled Markov processes  ... 
doi:10.46298/lmcs-18(2:19)2022 fatcat:5ssu52dnafbcdkflktwoyd6b5q

Modal Characterisations of Behavioural Pseudometrics [article]

Yuxin Deng, Wenjie Du, Daniel Gebler
2015 arXiv   pre-print
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  ...  We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic.  ...  Furthermore, van Breugel et al. propose an algorithm to approximate a behavioural pseudometric without discount [vBSW08].  ... 
arXiv:1509.03391v1 fatcat:vwray5n6tvadvgqv2hlpndl4p4

Characteristic Logics for Behavioural Hemimetrics via Fuzzy Lax Extensions [article]

Paul Wild, Lutz Schröder
2022 arXiv   pre-print
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  ...  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.  ...  Like their two-valued counterparts, behavioural distances have been introduced for quite a range of system types, such as various forms of probabilistic labelled transition systems or labelled Markov processes  ... 
arXiv:2007.01033v6 fatcat:sdxq3y2ylferpjhcgaobdqnapq

Polynomial-time Algorithms for Computing Distances of Fuzzy Transition Systems [article]

Taolue Chen, Tingting Han, Yongzhi Cao
2017 arXiv   pre-print
Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature.  ...  We then provide polynomial-time algorithms to calculate the behavioural distances, in both the non-discounted and the discounted setting. The algorithm is strongly polynomial in the former case.  ...  CONCLUSION We have studied the algorithmic aspect of behavioural distance for fuzzy transition systems.  ... 
arXiv:1701.06644v1 fatcat:7pq35mpw5zaz7mxoc2tmliew5a

Behavioural Pseudometrics for Nondeterministic Probabilistic Systems [chapter]

Wenjie Du, Yuxin Deng, Daniel Gebler
2016 Lecture Notes in Computer Science  
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  ...  We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic.  ...  Acknowledgement We thank the anonymous referees for their helpful comments. References  ... 
doi:10.1007/978-3-319-47677-3_5 fatcat:7tcqhmhlvzcuph5bp6wgidqage
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