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Bisimulation is two-way simulation

1994
*
Information Processing Letters
*

We give here a simple proof of the fact that on transition systems

doi:10.1016/0020-0190(94)00165-0
fatcat:i3ycwgdc65c3pemqtrmjiwvrhm
*bisimulation**is*the equivalence relation generated by*simulation*via functions. ... Consequently,(Id, Ur$) o T' 2 T o ( Ido u+)In a similar*way*one may prove that P H$ P". 0Theorem.*Bisimulation**is*the equivalence relation generated by*simulation*via functions. ... To this end we show that ( 1)*bisimulation*via functions coincides with*simulation*via functions and (2) for*two*bisimilar processes one may find a common refinement which*is*bisimilar via functions ...##
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Constrained Simulations, Nested Simulation Semantics and Counting Bisimulations

2008
*
Electronical Notes in Theoretical Computer Science
*

Nested

doi:10.1016/j.entcs.2008.03.074
fatcat:fhp7tktrsfdn5jcodzijm7zxhu
*simulations*define an interesting hierarchy of semantic preorders and equivalences in which every semantics refines the previous one and it*is*refined by the following. ... in terms of a*bisimulation*-like game. ... This*way*we will be playing a*bisimulation*-like game all the time: first the counting*bisimulation*and, at the end, the*bisimulation*up-to*simulation*. ...##
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New Bisimulation Semantics for Distributed Systems
[chapter]

2007
*
Lecture Notes in Computer Science
*

The main virtue of all these semantics

doi:10.1007/978-3-540-73196-2_10
fatcat:rg3dyhvvmjfb3biazc2lztkfaa
*is*that they are real*bisimulation*semantics, thus inheriting most of the good properties of*bisimulation*semantics. ... This*is*so because they can be defined as particular instances of Jacobs and Hughes' categorical definition of*simulation*, which they have already proved to satisfy all those properties. ...*Simulations*are one of the first natural*ways*to relax the definition of*bisimulation*. ...##
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Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations
[chapter]

2008
*
Lecture Notes in Computer Science
*

Our concrete objective

doi:10.1007/978-3-540-68855-6_18
fatcat:jm5jp66qjndnbnezuqb2mrmreq
*is*to present both ordinary*bisimulations*and probabilistic*bisimulations*in a common coalgebraic framework based on multiset*bisimulations*. ... We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial*way*, and extend all these results to categorical*simulations*... Natural transformations and*bisimulations*Natural transformations are the natural*way*to relate*two*functors. ...##
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Bisimulations Up-to for the Linear Time Branching Time Spectrum
[chapter]

2005
*
Lecture Notes in Computer Science
*

It

doi:10.1007/11539452_23
fatcat:kc6c5o5ghngy7lsuvtpqqqpgsq
*is*remarkable that the adequate orientation of the ordering relation*is*crucial to get this result. ... In order to get coinductive characterisations of those semantic equivalences that are weaker than strong*bisimulation*we use a variant of the*bisimulation*up-to technique in which we allow the use of a ...*bisimulation*instead of*two**simulations*t S v and v S t. ...##
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COMPOSED BISIMULATION FOR TREE AUTOMATA

2009
*
International Journal of Foundations of Computer Science
*

Composed

doi:10.1142/s0129054109006814
fatcat:qf6hgbc2h5hq5l6agd6jzy4ezq
*bisimulation**is*defined in terms of*two*different relations, namely upward and downward*bisimulation*. ...*is*not significantly more difficult to compute (and hence stays below the computational requirements of*simulation*-based reductions). ... In all our test cases, backward*bisimulation*followed by forward*bisimulation*behaves in a very similar*way*to composed*bisimulation*. ...##
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Fair Equivalence Relations
[chapter]

2000
*
Lecture Notes in Computer Science
*

In a

doi:10.1007/3-540-44450-5_12
fatcat:dabexamcufepljiawgjdbs6psm
*bisimulation*relation between © and © with no fairness,*two*related states and ¡ -calculus*is*given in [HR00]. 2 As shown in [ASB ¢ 94], the logic CTL induces yet another definition, strictly weaker ... For all types © of*bisimulation*relations (that*is*© F § $ t $¨ u ), a © -*bisimulation*relation !*is*© -stronger than ! % E to indicate that ...*Two*-*way**simulation**is*a useful criterion: and are*two*-*way*similar iff for every system we have w iff B and w iff V . ...##
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Fair Equivalence Relations
[chapter]

2003
*
Lecture Notes in Computer Science
*

In a

doi:10.1007/978-3-540-39910-0_30
fatcat:6c7kpqyb2vbhlmpbm43jbvbf5i
*bisimulation*relation between © and © with no fairness,*two*related states and ¡ -calculus*is*given in [HR00]. 2 As shown in [ASB ¢ 94], the logic CTL induces yet another definition, strictly weaker ... For all types © of*bisimulation*relations (that*is*© F § $ t $¨ u ), a © -*bisimulation*relation !*is*© -stronger than ! % E to indicate that ...*Two*-*way**simulation**is*a useful criterion: and are*two*-*way*similar iff for every system we have w iff B and w iff V . ...##
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Categorical Interpretation of Modal Structures under Bisimulation

2019
*
Kairos: Journal of Philosophy & Science
*

Then, we offer a sketch of categorical interpretation of

doi:10.2478/kjps-2019-0008
fatcat:yy4v6cfb3jednftyq73d2qitui
*bisimulation*between modal structures, which comprise both the structure and the valuation from a propositional language. ... In this work we summarise the concept of*bisimulation*, widely used both in computational sciences and in modal logic, that characterises modal structures with the same behaviour in terms of accessibility ...*Two*structures are bisimilar if there*is*a non trivial (non-empty)*bisimulation*between them, that*is*, if there are*two*mutual*simulations*between them. ...##
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Fuzzy Simulations and Bisimulations between Fuzzy Automata
[article]

2022
*
arXiv
*
pre-print

We prove that the fuzzy language recognized by a fuzzy automaton

arXiv:2205.01955v1
fatcat:2rpc672rmfdnna7zwoav7a7lea
*is*fuzzily preserved by fuzzy*simulations*and fuzzily invariant under fuzzy*bisimulations*. ... We also prove that the notions of fuzzy*simulation*and*bisimulation*have the Hennessy-Milner properties, which are a logical characterization of the greatest fuzzy*simulation*or*bisimulation*between*two*... ) between*two*fuzzy automata*is*also a fuzzy*simulation*(respectively,*bisimulation*) between them, but not vice versa. ...##
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(Bi)simulations up-to characterise process semantics

2009
*
Information and Computation
*

In particular, we have shown that the

doi:10.1016/j.ic.2007.12.003
fatcat:jtgbwaht75cebfdh5tjy6td5yq
*simulation*up-to an equivalence relation*is*a canonical preorder whose kernel*is*the given equivalence relation. ... The relation between*bisimulations*up-to and*simulations*up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders. ... If we consider the*way*classical*bisimulations*are defined we observe that there*is*first a (symmetric) local condition that relates the sets of initial actions of any*two*related processes, which*is*mainly ...##
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Nondeterministic automata: equivalence, bisimulations, and uniform relations
[article]

2011
*
arXiv
*
pre-print

For each od these three types of

arXiv:1102.5449v1
fatcat:p5lu2uasujhmdmof2lzgyfo3ku
*bisimulations*we provide a procedure which decides whether there*is*a*bisimulation*of this type between*two*automata, and when it exists, the same procedure computes the ... We also show that there*is*a uniform forward*bisimulation*between*two*automata if and only if the factor automata with respect to the greatest forward*bisimulation*equivalences on these automata are isomorphic ... The first of them*is*a theorem that gives a*way*to decide whether there*is*a weak forward*simulation*between*two*automata, and whenever it exists, provides a*way*to construct the greatest one. ...##
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Global Timed Bisimulation: An Introduction
[chapter]

1999
*
IFIP Advances in Information and Communication Technology
*

Global timed

doi:10.1007/978-0-387-35578-8_23
fatcat:h5thi6igq5eufhu7b5oidn7kpa
*bisimulation**is*defined exactly as weak timed*bisimulation*once ordinary transitions are replaced by the adequate notions of generalized transitions. ... Unfortunately, this*is*not fully accomplished: for instance, the internal choice operator becomes non-associative since*bisimulation*can see the branching structure of processes. ... But these internal actions must be treated in a special*way*in order to capture the fact that they are not observable. This*is*why a weaker notion of*bisimulation**is*introduced: weak*bisimulation*. ...##
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Equivalence of Dynamical Systems by Bisimulation

2004
*
IEEE Transactions on Automatic Control
*

A characterization of

doi:10.1109/tac.2004.838497
fatcat:sunuwnii6rejfexwgelqfpswrq
*bisimulation*and an algorithm for computing the maximal*bisimulation*relation*is*derived using geometric control theory. ... The notion of*bisimulation**is*especially powerful for "nondeterministic" dynamical systems, and leads in this case to a notion of equivalence which*is*finer than equality of external behavior. ... Hence, , which*is*by Proposition 5.3 a*bisimulation*relation, and thus contained in . Since*is*also a*simulation*relation equality follows. ...##
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Analysing and Comparing Encodability Criteria

2015
*
Electronic Proceedings in Theoretical Computer Science
*

relation (coupled

doi:10.4204/eptcs.190.4
fatcat:qtqir242zva73h363kajbkvsyi
*simulation*versus*bisimulation*) that*is*induced by different variants of operational correspondence. ... Encodings or the proof of their absence are the main*way*to compare process calculi. ... R*is*a*bisimulation*if any*two*related processes mutually*simulate*their respective sequences of steps, such that the derivatives are again related. ...
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