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From rewrite rules to bisimulation congruences

Peter Sewell
2002 Theoretical Computer Science  
They give rise to bisimulation congruences. As a test of the theory it is shown that bisimulation for a fragment of CCS is recovered.  ...  General deÿnitions of labelled transitions are given in each case, uniformly in the set of rewrite rules, and without requiring the prescription of additional notions of observation.  ...  show how the indexed structure of labelled transitions arises from the rewrite rules and structural congruence.  ... 
doi:10.1016/s0304-3975(00)00309-1 fatcat:sldo43va3rgc5dk5i3vd2rduzm

Observational Equivalence for Synchronized Graph Rewriting with Mobility [chapter]

Barbara König, Ugo Montanari
2001 Lecture Notes in Computer Science  
One of the main results of the paper says that bisimilarity for synchronized graph rewriting is a congruence whenever the rewriting rules satisfy the basic source property.  ...  We introduce a notion of bisimulation for graph rewriting systems, allowing us to prove observational equivalence for dynamically evolving graphs and networks.  ...  Acknowledgements: We would like to thank Roberto Bruni and Dan Hirsch for their help.  ... 
doi:10.1007/3-540-45500-0_7 fatcat:miux6zxvljgeljhdodmjaw7lgy

From Active Names to π-calculus Rewriting Rules

Ana C.V. de Melo
2005 Electronical Notes in Theoretical Computer Science  
There, agents active names are calculated from their corresponding Labelled Transition Systems (LTS) and, because of this, cannot be directly applied to rewriting systems.  ...  This result and a technique to check bisimulation considering active names is presented in [7] .  ...  Bisimulation checking can be performed by rewriting rules concerned with structural congruence.  ... 
doi:10.1016/j.entcs.2005.03.010 fatcat:elaf7o6tcvgklnc67lztsuhuge

Bisimulations in calculi modelling membranes

Roberto Barbuti, Andrea Maggiolo-Schettini, Paolo Milazzo, Angelo Troina
2008 Formal Aspects of Computing  
These two formalisms are the Calculus of Looping Sequences (CLS) and Brane Calculi, and since they stem from two different approaches (rewrite systems and process calculi) bisimulation appears to be a  ...  We introduce CLS and define a labelled semantics and bisimulations for which we prove some congruence results.  ...  From a technical point of view, the first case study shows how to modify rewrite rules of a model in order to observe an internal event from outside, whereas the second case study shows that bisimulations  ... 
doi:10.1007/s00165-008-0071-x fatcat:5yrobr5vhjb3vdd2ayofly2roi

Iterating Transducers [chapter]

Dennis Dams, Yassine Lakhnech, Martin Steffen
2001 Lecture Notes in Computer Science  
We show how this extrapolation may be rephrased as a problem of detecting confluence properties of rewrite systems that represent the bisimulations.  ...  Thus, we can draw upon techniques that have been developed in the area of rewriting. A prototype implementation has been successfully applied to various examples.  ...  Acknowledgements We like to thank the anonymous referees for their careful work and their valuable and insightful comments and suggestions.  ... 
doi:10.1007/3-540-44585-4_27 fatcat:mevai4bbybafbpns6xi7lkrmyq

Modular Bisimulation Theory for Computations and Values [chapter]

Martin Churchill, Peter D. Mosses
2013 Lecture Notes in Computer Science  
Finally, we show how algebraic laws can be proved sound for bisimulation with reference only to the (M)SOS rules defining the programming constructs involved in them.  ...  For structural operational semantics (SOS) of process algebras, various notions of bisimulation have been studied, together with rule formats ensuring that bisimilarity is a congruence.  ...  Many thanks to Mohammad Mousavi, Cristian Prisacariu, Paolo Torrini and the anonymous referees for their useful comments.  ... 
doi:10.1007/978-3-642-37075-5_7 fatcat:vox2zuovdreitaingtoxx3bzlm

Bisimulation Congruences in the Calculus of Looping Sequences [chapter]

Roberto Barbuti, Andrea Maggiolo-Schettini, Paolo Milazzo, Angelo Troina
2006 Lecture Notes in Computer Science  
We define bisimulation relations that are congruences with respect to the operators on terms, and we show an application of CLS to the modeling of a biological system and we use bisimulations to reason  ...  CLS terms can be transformed by applying rewrite rules. We give a labeled transition semantics for CLS by using, as labels, contexts in which rules can be applied.  ...  As future work, we plan to develop a quantitative extension of the calculus in which speed of events are modeled as rates of rewrite rule applications.  ... 
doi:10.1007/11921240_7 fatcat:r2x3acfze5fwfhna6wmebfkh34

Iterating transducers

Dennis Dams, Yassine Lakhnech, Martin Steffen
2002 The Journal of Logic and Algebraic Programming  
Thus, we can draw upon techniques from the area of rewriting. A prototype implementation has been successfully applied to various examples.  ...  We show how this extrapolation may be rephrased as a problem of detecting confluence properties of rewrite systems that represent the bisimulations.  ...  Furthermore thanks to Kedar Namjoshi, Kai Baukus, and Karsten Stahl for inspiring discussions and suggestions, and careful reading of earlier versions of this document.  ... 
doi:10.1016/s1567-8326(02)00025-5 fatcat:oesc7b2evvdqnmxhcjepz2n63m

Bisimulation collapse and the process taxonomy [chapter]

Olaf Burkart, Didier Caucal, Bernhard Steffen
1996 Lecture Notes in Computer Science  
We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence.  ...  Since finiteness of regular graphs is decidable, this yields, as a corollary, a decision procedure for the finiteness problem of context-free processes wrt. bisimulation equivalence.  ...  If the rewrite rules R are of the form V • 27 x V* the rewrite system is called alphabetic. In the remainder of the paper, a rewrite rule (u, a, v) E R is also written as u -% v.  ... 
doi:10.1007/3-540-61604-7_59 fatcat:544p6qedefgubacn3bvciado3q

Higher category models of the pi-calculus [article]

Mike Stay, Lucius Gregory Meredith
2015 arXiv   pre-print
The interpretation is consistent with Curry-Howard, interpreting terms as typed morphisms, while simultaneously providing an explicit interpretation of the rewrite rules of standard operational presentations  ...  One of the key contributions, inspired by catalysis in chemical reactions, is a method of restricting the application of 2-morphisms interpreting rewrites to specific contexts.  ...  of this work; and Marius Buliga for some initial conversations which prompted us to reconsider enzymatic-style solutions.  ... 
arXiv:1504.04311v4 fatcat:hsyzpfynszgbpgq454dozcehfq

Conditional Bisimilarity for Reactive Systems

Mathias Hülsbusch, Barbara König, Sebastian Küpper, Lars Stoltenow, Zena M. Ariola
2020 International Conference on Formal Structures for Computation and Deduction  
Reactive systems à la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences.  ...  We instantiate reactive systems in order to obtain DPO graph rewriting and consider a case study in this setting.  ...  bisimulation congruences.  ... 
doi:10.4230/lipics.fscd.2020.10 dblp:conf/fscd/Hulsbusch0KS20 fatcat:xiv56r3h2za5fedg2ws5yp6crq

A complete equational axiomatization for prefix iteration

Wan Fokkink
1994 Information Processing Letters  
To obtain this result, we set up a term rewriting system, based on the axioms, and show that bisimilar terms have the same normal form.  ...  We present a finite equational axiomatization for MPA * δ , and prove that this axiomatization is complete with respect to strong bisimulation equivalence.  ...  A standard scheme for such a proof is to set up a Term Rewriting System (TRS) from the axioms as follows. 1. Turn the axioms into rewrite rules. 2.  ... 
doi:10.1016/0020-0190(94)00163-4 fatcat:kmsqmee6l5czfmkvzpwq6iw47e

Actions speak louder than words: proving bisimilarity for context-free processes

H Huttel
1998 Journal of Logic and Computation  
We also show how to obtain a sound and complete sequent-based equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful  ...  In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goal-directed rules.  ...  We must rewrite X and can then add (Y; (X ) # R) to R. This is the basis of the rule UPDATE. The rule REWRITE tells us that we must rewrite using R whenever possible.  ... 
doi:10.1093/logcom/8.4.485 fatcat:sfffqqvwdbfmjpicymyaojyms4

Using a generalisation critic to find bisimulations for coinductive proofs [chapter]

Louise Dennis, Alan Bundy, Ian Green
1997 Lecture Notes in Computer Science  
Through the use of bisimulations and proofs that observational equivalence is a congruence in various domains it can be used to proof the congruence of two processes.  ...  Crucially they require the user to supply an appropriate relation which the system can then prove to be a bisimulation.  ...  rewrite rules e.g.  ... 
doi:10.1007/3-540-63104-6_29 fatcat:jt576rkiibdzdkdzihvghsexoe

Deriving Bisimulation Congruences for Conditional Reactive Systems [chapter]

Mathias Hülsbusch, Barbara König
2012 Lecture Notes in Computer Science  
We study the problem of deriving labelled transitions and bisimulation congruences from a reduction semantics.  ...  We consider conditional reactive systems, a general abstract framework for rewriting, in which reactive systemsà la Leifer and Milner are enriched with (nested) application conditions.  ...  We would like to thank Vladimiro Sassone for asking an inspiring question after a talk.  ... 
doi:10.1007/978-3-642-28729-9_24 fatcat:v4favowrdrhbdalovdapmhrzve
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