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An automata theoretic decision procedure for the propositional mu- calculus. (English) Zbl 0671.03023

A decision procedure of elementary complexity is presented for the propositional mu-calculus. This calculus was introduced by D. Kozen as a powerful generalization of propositional dynamic logic, in which, in particular, Streett’s infinite repeating construction \(\Delta\) \(a\) can be expressed. The proof is based on using tree automata and strengthens a result by D. Kozen and R. Parikh on (non-elementary) decidability of the mu-calculus obtained by reduction to the monadic second order theory of many successors.
Reviewer: M.K.Valiev

MSC:

03B70 Logic in computer science
68N01 General topics in the theory of software
03B25 Decidability of theories and sets of sentences
68Q65 Abstract data types; algebraic specification
03D05 Automata and formal grammars in connection with logical questions
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