Synonyms
Definition
Bisimulation equivalence is a semantic equivalence relation on labeled transition systems, which are used to represent distributed systems. It identifies systems with the same branching structure.
Discussion
Labeled Transition Systems
A labeled transition system consists of a collection of states and a collection of transitions between them. The transitions are labeled by actions from a given set A that happen when the transition is taken, and the states may be labeled by predicates from a given set P that hold in that state.
Definition 1
Let A and P be sets (of actions and predicates, respectively).
A labeled transition system (LTS) over A and P is a triple \((S,\rightarrow,\models )\) with:
S a class (of states).
→ a collection of binary relations \({\mathop \rightarrow \limits ^{a}}\; \subseteq S \times S\) – one for every a ∈ A – (the transitions),such that for all s ∈ S the class \(\{t \in S\mid s{\mathop \rightarrow...
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Bibliography
Aczel P (1988) Non-well-founded Sets, CSLI Lecture Notes 14. Stanford University, Stanford, CA
van Glabbeek RJ (1990) Comparative concurrency semantics and refinement of actions. PhD thesis, Free University, Amsterdam. Second edition available as CWI tract 109, CWI, Amsterdam 1996
Hennessy M, Milner R (1985) Algebraic laws for nondeterminism and concurrency. J ACM 32(1):137–161
Hollenberg MJ (1995) Hennessy-Milner classes and process algebra. In: Ponse A, de Rijke M, Venema Y (eds) Modal logic and process algebra: a bisimulation perspective, CSLI Lecture Notes 53, CSLI Publications, Stanford, CA, pp 187–216
Milner R (1990) Operational and algebraic semantics of concurrent processes. In: van Leeuwen J (ed) Handbook of theoretical computer science, Chapter 19. Elsevier Science Publishers B.V., North-Holland, pp 1201–1242
Further Reading
Baeten JCM, Weijland WP (1990) Process algebra. Cambridge University Press
Milner R (1989) Communication and concurrency. Prentice Hall, New Jersey
Sangiorgi D (2009) on the origins of bisimulation and coinduction. ACM Trans Program Lang Syst 31(4). doi: 10.1145/1516507.1516510
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van Glabbeek, R.J. (2011). Bisimulation. In: Padua, D. (eds) Encyclopedia of Parallel Computing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09766-4_149
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DOI: https://doi.org/10.1007/978-0-387-09766-4_149
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