Automata-Theoretic Characterisations of Branching-Time Temporal Logics

TL;DR

This paper provides automata-theoretic characterisations of key branching-time temporal logics, expanding the understanding of their expressive power and solving a long-standing open problem in the field.

Contribution

It introduces two variants of Hesitant Tree Automata that are equivalent to CTL* and ECTL* on arbitrary-branching trees, broadening the automata-theoretic framework for branching-time logics.

Findings

Automata-theoretic characterisations of CTL* and ECTL* on arbitrary-branching trees.

Identification of two variants of Hesitant Tree Automata equivalent to these logics.

Resolution of a forty-year-old open question in the field.

Abstract

Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete connections have been established for the linear-time case between temporal logics, predicate logics, algebraic models, and automata, the situation in the branching-time case remains considerably more fragmented. In this work, we provide an automata-theoretic characterisation of some important branching-time temporal logics, namely CTL* and ECTL* interpreted on arbitrary-branching trees, by identifying two variants of Hesitant Tree Automata that are proved equivalent to those logics. The characterisations also apply to Monadic Path Logic and the bisimulation-invariant fragment of Monadic Chain Logic, again interpreted over trees. These results widen the characterisation landscape of the branching-time case and solve a forty-year-old open question.