A Subclass of Mu-Calculus with the Freeze Quantifier Equivalent to Buchi 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 mu$^\downarrow$-calculus, which is a subclass of modal mu-calculus with the freeze quantifier, and showed that it has the same expressive power as RA. However, disjunctive mu$^\downarrow$-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 disjunctive mu$^\downarrow$-calculus to be suitable for infinite words and prove that the obtained temporal logic has the same expressive power as Buchi RA.