Propositional Dynamic Logic of looping and converse

Authors:
Robert S. Streett
Affiliations:
-
Venue:
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Year:
1981

Citing 2
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Abstract

Propositional Dynamic Logic can be extended to include both an infinitary iteration construct delta and a backtracking construct converse. The resulting logic does not satisfy the finite model property, but is nevertheless elementarily decidable. In order to establish this decidability result, deterministic two-way automata on infinite trees are defined and shown to be reducible to nondeterministic one-way automata on infinite trees. The decision procedure suggests a nonstandard semantics for the extended logic for which the finite model property does hold.