Abstract
Expressions involving least and greatest fixed point operators are interpreted in the power-set algebra of (possibly infinite) trees and also in some abstract models. Initiality of the tree algebra is established via a "Mezei-and Wright-like" result on interpretation of fixed point terms. Then a reduction of these terms to Rabin automata on infinite trees is shown which yields some decidability results. A connection is exhibited between the hierarchy of alternating least and greatest fixed points and the hierarchy of Rabin pair indices of automata.
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References
Arnold, A. & Nivat, M. (1977), Non deterministic recursive programs, in "Fundamentals of Computation Theory", pp. 12â21, LNCS No. 56, Springer Verlag, Heidelberg.
deBakker, J. & deRoever, W.P. (1973), A Calculus for Recursive Program Schemes, First Int.Coll.on Automata, Languages and Programming.
Emerson, A.E. & Clarke, E.C. (1980), Characterizing Correctness Properties of Parallel Programs using Fixpoints, Seventh Int.Coll. on Automata, Languages and Programming, 169â181.
Engelfriet, J. & Schmidt, E.M. (1978), IO and OI, JCSS 15 (1977), 328â353 and 16 (1978), 67â99.
Kozen, D. (1983), Results on the Propositional ÎŒ-Calculus, TCS 27, 333â54.
NiwiĆski, D. (1984), Fixed-Point Characterization of Context-Free â-Languages, Inform. Contr. 61, 247â276.
NiwiĆski, D. (1985), Equational ÎŒ-calculus, in "Computation Theory", LNCS No. 208, Springer Verlag, Heidelberg.
NiwiĆski, D. (1986), A note on indices of Rabin pair automata, University of Warsaw, manuscript.
Park, D. (1980), On the semantics of fair parallelism, in "Abstract Software specifications", LNCS No. 86, Springer Verlag, Heidelberg.
Park, D. (1981), Concurrency and automata on infinite sequences, LNCS No. 104, Springer Verlag, Heidelberg, 167â183.
Rabin, M.O. (1969), Decidability os second-order theories and automata on infinite trees, in Trans. Amer. Math. Soc. 141, 1â35.
Rabin, M.O. (1970), Weakly definable relations and special automata, in Math. Logic and Found. of Set Theory (Ed. Bar-Hillel), North-Holland.
Rabin, M.O. (1972), Automata on Infinite Objects and Church's Problem, in Proc. Regional AMS Conf. Series in Math. 13, 1â22.
Takahashi, M. (1985), The Greatest Fixed-Points and Rational Omega-Tree Languages, Université Paris VII, manuscript.
Vardi, M.Y. & Wolper, P. (1984), Automata-theoretic Techniques for Modal Logic of Programs, Report RJ 4450, IBM Research, Yorktown Heights.
Wand, M. (1973), First Int.Coll. on Automata, Languages and Programming, 331â344.
McNaughton, R. (1966), Testing and generating infinite sequences by a finite automaton, Inform. Contr. 9, 521â530.
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© 1986 Springer-Verlag Berlin Heidelberg
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NiwiĆski, D. (1986). On fixed-point clones. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_96
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DOI: https://doi.org/10.1007/3-540-16761-7_96
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