A Linear-Time Nominal $\mu$-Calculus with Name Allocation

TL;DR

This paper introduces Bar-muTL, a linear-time fixpoint logic for infinite alphabet words, enabling efficient model checking and satisfiability despite the complexity of automata with name binding.

Contribution

It presents Bar-muTL, a novel logic with full negation and freeze quantification, and proves its model checking and satisfiability are elementary, extending the tractability of nominal automata.

Findings

Model checking in 2ExpSpace with parameterized complexity.

Satisfiability checking also has elementary complexity.

Reduction to extended RNNAs demonstrates tractability.

Abstract

Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as regular nondeterministic nominal automata (RNNAs) have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-muTL for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-muTL allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-muTL over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter.