Fair Bisimulation

ion with 5 states. However, for the Buchi structure K4 of Figure 2(b),fabs(K4) and K4 are not fairly bisimilar.It therefore remains an open problem to construct, in general, a minimalstructure which is fairly bisimilar to K (where minimality is measured in thenumber of states).References[ASB94] A. Aziz, V. Singhal, F. Balarin, R.K. Brayton, and A.L. Sangiovanni-Vincentelli. Equivalences for fair kripke structures. In S. Abiteboul andE. Shamir, editors, ICALP 94: International Colloquium on Automata, Lan-guages, and Programming, Lecture Notes in Computer Science 820, pages 364{375. Springer-Verlag, 1994.[BCG88] M.C. Browne, E.M. Clarke, and O. Grumberg. Characterizing nite Kripkestructures in propositional temporal logic. Theoretical Computer Science,59:115{131, 1988.[BKO87] J.A. Bergstra, J.W. Klop, and E.R. Olderog. Failures without chaos: a newprocess semantics for fair abstraction. In Formal Description Techniques III,pages 77{103. Elsevier, 1987.[BW90] J.C.M. Baeten and W.P. Weijland. Process Algebra. Cambridge UniversityPress, 1990.[CES86] E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic veri cation of nite-state concurrent systems using temporal-logic speci cations. ACM Transac-tions on Programming Languages and Systems, 8(2):244{263, 1986.[CPS93] R.J. Cleaveland, J. Parrow, and B. Ste en. The Concurrency Workbench: asemantics-based tool for the veri cation of nite-state systems. ACM Trans-actions on Programming Languages and Systems, 15(1):36{72, 1993.[EB95] W. Vogler E. Brinksma, A. Rensink. Fair testing. In I. Lee and S. Smolka,editors, CONCUR 95: Theories of Concurrency, Lecture Notes in ComputerScience 962, pages 313{327. Springer-Verlag, July 1995.[GL94] O. Grumberg and D.E. Long. Model checking and modular veri cation. ACMTransactions on Programming Languages and Systems, 16(3):843{871, 1994.[Hen87] M.C.B. Hennessy. An algebraic theory of fair asynchronous communicatingprocesses. Theretical Computer Science, 49:121{143, 1987.[HK96] M. Huth and M. Kwiatkowska. The semantics for fair recursion with diver-gence. Technical Report CSR-96-4, University of Birmingham, 1996.[HKR97] T.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. InCONCUR 97: Theories of Concurrency, Lecture Notes in Computer Science1243, pages 273{287. Springer-Verlag, July 1997.[KS90] P.C. Kanellakis and S.A. Smolka. CCS expressions, nite-state processes, andthree problems of equivalence. Information and Computation, 86:43{68, 1990.[KV96] O. Kupferman and M.Y. Vardi. Veri cation of fair transition systems. InR. Alur and T.A. Henzinger, editors, CAV 96: Computer Aided Veri cation,Lecture Notes in Computer Science 1102, pages 372{381. Springer-Verlag,1996.[KV98] O. Kupferman and M.Y. Vardi. Weak alternating automata and tree au-tomata emptiness. In Proceedings of the 30th ACM Symposium on Theory ofComputing, pages 224{233. ACM Press, 1998.[Mil89] R. Milner. Communication and Concurrency. Prentice-Hall, 1989.15 [NC95] V. Natarajan and R. Cleaveland. Divergence and fair testing. In ICALP'95: International Colloquium on Automata, Languages, and Programming,LectureNotes in Computer Science 944, pages 648{659. Springer-Verlag, 1995.[Par80] D.M.R. Park. Concurrency and Automata on In nite Sequences. LectureNotes in Computer Science 104. Springer-Verlag, 1980.[PT87] R. Paige and R.E. Tarjan. Three partition-re nement algorithms. SIAMJournal of Computing, 16(6):973{989, 1987.