Contents 1 Preface 22 Algebraic Theory of Regular Languages 22
نویسنده
چکیده
from [TW96]) We reveal an intimate connection between semidirect products of nite 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 k in the `until' operator. Applying deep results from nite semigroup theory we are able to prove that each level of the `until' hierarchy is decidable.
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