Abstract
Bergstra, Ponse and van der Zwaag introduced in 2003 the notion of orthogonal bisimulation equivalence on labeled transition systems. This equivalence is a refinement of branching bisimulation, in which consecutive tau’s (silent steps) can be compressed into one (but not zero) tau’s. The main advantage of orthogonal bisimulation is that it combines well with priorities. Here we solve the problem of deciding orthogonal bisimulation equivalence in finite (regular) labeled transition systems. Unlike as in branching bisimulation, in orthogonal bisimulation, cycles of silent steps cannot be eliminated. Hence, the algorithm of Groote and Vaandrager (1990) cannot be adapted easily. However, we show that it is still possible to decide orthogonal bisimulation with the same complexity as that of Groote and Vaandrager’s algorithm. Thus if n is the number of states, and m the number of transitions then it takes O(n(m + n)) time to decide orthogonal bisimilarity on finite labeled transition systems, using O(m + n) space.
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Aho AV, Hopcroft JE, Ullman JD (1974) The design and analysis of computer algorithms. Addison-Wesley, Reading
Browne MC, Clarke EM, Grumberg O (1988) Characterizing finite Kripke structure in propositional temporal logic. Theor Comput Sci 59(1–2):115–131
Baeten JCM, van Glabbeek RJ (1987) Another look at abstraction in process algebra. In: Ottmann Th (ed) ICALP 87, Vol 267 of Lecture Notes in Computer Science, Springer, Heidelberg, pp 84–94
Bergstra JA, Ponse A, van der Zwaag MB (2003) Branching time and orthogonal bisimulation equivalence. Theor Comput Sci 309:313–355
van Glabbeek RJ (1994) What is branching time semantics and why to use it?. Bull EATCS 53:190–198
Groote JF, Vaandrager FW (1990) An efficient algorithm for branching bisimulation and stuttering equivalence. In: Paterson MS (ed), ICALP 90, Vol 443 of Lecture Notes in Computer Science. Springer, Heidelberg, pp 626–638
van Glabbeek RJ, Weijland WP (1996) Branching time and abstraction in bisimulation semantics. J ACM 43:555–600
Hennessy M, Milner R (1985) Algebraic laws for nondeterminism and concurrency. J ACM 32:137–161
Milner R (1980) A calculus of communicating systems, Vol 92 of Lecture Notes in Computer Science. Springer, Heidelberg
Milner R (1981) A modal characterisation of observable machine behaviour. In: Astesiano G, Böhm C (eds), CAAP 81, Vol 112 of Lecture Notes in Computer Science. Springer, Heidelberg, pp 25–34
Paige R, Tarjan R (1987) Three partition refinement algorithms. SIAM J Comput 16(6):973–989
Vu TD (2005) The compression structure of a process. Inf Process Lett 96:225–229
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J. Parrow
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Vu, T.D. Deciding orthogonal bisimulation. Form Asp Comp 19, 475–485 (2007). https://doi.org/10.1007/s00165-007-0023-x
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DOI: https://doi.org/10.1007/s00165-007-0023-x