On the expressivity of the modal mu-calculus
We analyse the complexity of the sets of states, in certain classes of infinite systems, that satisfy formulae of the modal mu-calculus. Improving on some of our earlier results, we establish a strong upper bound (namely Δ 2 1 ). We also establish various lower bounds and restricted upper bounds, incidentally providing another proof that the mu-calculus alternation hierarchy does not collapse at level 2.
Keywordsdescriptive complexity logic in computer science verification temporal logic
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- [ArN90]A. Arnold and D. Niwinski, Fixed point characterization of Büchi automata on infinite trees. J. Inf. Process. Cybern., EIK 26, 451–459 (1990).Google Scholar
- [Bra91]J. C. Bradfield, Verifying Temporal Properties of Systems. Birkhäuser, Boston, Mass. ISBN 0-8176-3625-0 (1991).Google Scholar
- [Bra92]J. C. Bradfield, A proof assistant for symbolic model-checking. Proc. CAV '92. LNCS 663 316–329 (1993).Google Scholar
- [Bra95]J. C. Bradfield, On the expressivity of the modal mu-calculus, Technical Report ECS-LFCS-95-338, LFCS, University of Edinburgh (1995). On-line via http://www.dcs.ed.ac.uk/home/jcb/.Google Scholar
- [EmL86]E. A. Emerson and C.-L. Lei, Efficient model checking in fragments of the propositional mu-calculus. Proc. First IEEE Symp. on Logic in Computer Science 267–278 (1986).Google Scholar
- [Esp94]J. Esparza, On the decidability of model-checking for several μ-calculi and Petri nets, Proc. CAAP '94, LNCS 787 115–129 (1994).Google Scholar
- [EsN94]J. Esparza and M. Nielsen, Decidability issues for Petri nets — a survey, J. Inform. Process. Cybernet. 30 143–160 (1994).Google Scholar
- [Mos80]Y. N. Moschovakis, Descriptive set theory. North-Holland, Amsterdam & New York (1980).Google Scholar
- [Niw86]D. Niwiński, On fixed point clones. Proc. 13th ICALP, LNCS 226 464–473 (1986).Google Scholar
- [Rab70]M. O. Rabin, Weakly definable relations and special automata, in Y. Bar-Hillel (ed.) Mathematical Logic and Foundations of Set Theory, North-Holland, Amsterdam (1970), 1–23.Google Scholar