Interval temporal logic and star-free expressions

Abstract

The connection between temporal logic, first-order logic and formal language theory is well known in the context of propositional temporal logic (PTL). In the present paper the situation is analyzed for the propositional interval temporal logic (ITL), which has been used for the specification of digital circuits. In contrast to PTL the propositional variables of ITL formulas are interpreted in sequences of states (intervals) instead of a single state. This motivates a calculus of star-free regular expressions with a new interpretation of the basic constants (by words instead of letters). We will show here that ITL is strictly more expressive than this calculus of star-free expressions, but strictly less expressive than a corresponding first-order language. For the proof we use a modification of the Ehrenfeucht-Fraisse games, capturing the expressive power of the extended star-free expressions.