A Subclass of Mu-Calculus with the Freeze Quantifier Equivalent to Büchi Register Automata

Abstract

Register automaton (RA) is an extension of finite automaton for dealing with data values in an infinite domain. In the previous work, we proposed disjunctive μ^↓-calculus (μ^↓_d-calculus), which is a subclass of modal µ-calculus with the freeze quantifier, and showed that it has the same expressive power as RA. However, μ^↓_d-calculus is defined as a logic on finite words, whereas temporal specifications in model checking are usually given in terms of infinite words. In this paper, we re-define the syntax and semantics of μ^↓_d-calculus to be suitable for infinite words and prove that the obtained temporal logic, called μ^↓_dω-calculus, has the same expressive power as Büchi RA.