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Bisimulation is two-way simulation

J.A. Bergstra, Gh. Ştefănescu
1994 Information Processing Letters  
We give here a simple proof of the fact that on transition systems 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  ... 
doi:10.1016/0020-0190(94)00165-0 fatcat:i3ycwgdc65c3pemqtrmjiwvrhm

Constrained Simulations, Nested Simulation Semantics and Counting Bisimulations

David de Frutos Escrig, Carlos Gregorio Rodríguez
2008 Electronical Notes in Theoretical Computer Science  
Nested 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.  ... 
doi:10.1016/j.entcs.2008.03.074 fatcat:fhp7tktrsfdn5jcodzijm7zxhu

New Bisimulation Semantics for Distributed Systems [chapter]

David de Frutos-Escrig, Fernando Rosa-Velardo, Carlos Gregorio-Rodríguez
2007 Lecture Notes in Computer Science  
The main virtue of all these semantics 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.  ... 
doi:10.1007/978-3-540-73196-2_10 fatcat:rg3dyhvvmjfb3biazc2lztkfaa

Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations [chapter]

David de Frutos Escrig, Miguel Palomino, Ignacio Fábregas
2008 Lecture Notes in Computer Science  
Our concrete objective 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.  ... 
doi:10.1007/978-3-540-68855-6_18 fatcat:jm5jp66qjndnbnezuqb2mrmreq

Bisimulations Up-to for the Linear Time Branching Time Spectrum [chapter]

David de Frutos Escrig, Carlos Gregorio Rodríguez
2005 Lecture Notes in Computer Science  
It 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.  ... 
doi:10.1007/11539452_23 fatcat:kc6c5o5ghngy7lsuvtpqqqpgsq

COMPOSED BISIMULATION FOR TREE AUTOMATA

PAROSH AZIZ ABDULLA, AHMED BOUAJJANI, LUKÁŠ HOLÍK, LISA KAATI, TOMÁŠ VOJNAR
2009 International Journal of Foundations of Computer Science  
Composed 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.  ... 
doi:10.1142/s0129054109006814 fatcat:qf6hgbc2h5hq5l6agd6jzy4ezq

Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2000 Lecture Notes in Computer Science  
In a 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 .  ... 
doi:10.1007/3-540-44450-5_12 fatcat:dabexamcufepljiawgjdbs6psm

Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2003 Lecture Notes in Computer Science  
In a 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 .  ... 
doi:10.1007/978-3-540-39910-0_30 fatcat:6c7kpqyb2vbhlmpbm43jbvbf5i

Categorical Interpretation of Modal Structures under Bisimulation

Nino Guallart
2019 Kairos: Journal of Philosophy & Science  
Then, we offer a sketch of categorical interpretation of 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.  ... 
doi:10.2478/kjps-2019-0008 fatcat:yy4v6cfb3jednftyq73d2qitui

Fuzzy Simulations and Bisimulations between Fuzzy Automata [article]

Linh Anh Nguyen
2022 arXiv   pre-print
We prove that the fuzzy language recognized by a fuzzy automaton 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.  ... 
arXiv:2205.01955v1 fatcat:2rpc672rmfdnna7zwoav7a7lea

(Bi)simulations up-to characterise process semantics

David de Frutos Escrig, Carlos Gregorio Rodríguez
2009 Information and Computation  
In particular, we have shown that the 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  ... 
doi:10.1016/j.ic.2007.12.003 fatcat:jtgbwaht75cebfdh5tjy6td5yq

Nondeterministic automata: equivalence, bisimulations, and uniform relations [article]

Miroslav Ćirić, Jelena Ignjatović, Milan Bašić, Ivana Jančić
2011 arXiv   pre-print
For each od these three types of 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.  ... 
arXiv:1102.5449v1 fatcat:p5lu2uasujhmdmof2lzgyfo3ku

Global Timed Bisimulation: An Introduction [chapter]

David de Frutos-Escrig, Natalia López, Manuel Núñez
1999 IFIP Advances in Information and Communication Technology  
Global timed 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.  ... 
doi:10.1007/978-0-387-35578-8_23 fatcat:h5thi6igq5eufhu7b5oidn7kpa

Equivalence of Dynamical Systems by Bisimulation

A. vanderSchaft
2004 IEEE Transactions on Automatic Control  
A characterization of 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.  ... 
doi:10.1109/tac.2004.838497 fatcat:sunuwnii6rejfexwgelqfpswrq

Analysing and Comparing Encodability Criteria

Kirstin Peters, Rob van Glabbeek
2015 Electronic Proceedings in Theoretical Computer Science  
relation (coupled 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.  ... 
doi:10.4204/eptcs.190.4 fatcat:qtqir242zva73h363kajbkvsyi
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