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Temporal logic and semidirect products: an effective characterization of the until hierarchy

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2 Author(s)
Therien, D. ; Sch. of Comput. Sci., McGill Univ., Montreal, Que., Canada ; Wilke, T.

We reveal an intimate connection between semidirect products of finite semigroups and substitution of formulas in linear temporal logic. We use this connection to obtain an algebraic characterization of the `until' hierarchy of linear temporal logic; the k-th level of that hierarchy is comprised of all temporal properties that are expressible by a formula of nesting depth at most k in the `until' operator. Applying deep results from finite semigroup theory we are able to prove that each level of the until hierarchy is decidable

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996