On the Complexity of Verifying Regular Properties on Flat Counter Systems

TL;DR

This paper analyzes the computational complexity of verifying various logical properties on flat counter systems, providing a comprehensive classification across different formal languages and complexity classes.

Contribution

It offers a detailed complexity characterization for model-checking problems on flat counter systems across multiple specification languages.

Findings

Complexity ranges from PTime to PSpace depending on the logic.

Results apply to languages with arithmetical constraints on counters.

Provides a uniform proof approach for the complexity analysis.

Abstract

Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is not always well studied except for reachability queries or for Past LTL. In this paper, we characterize the complexity of model-checking problems on flat counter systems for the specification languages including first-order logic, linear mu-calculus, infinite automata, and related formalisms. Our results span different complexity classes (mainly from PTime to PSpace) and they apply to languages in which arithmetical constraints on counter values are systematically allowed. As far as the proof techniques are concerned, we provide a uniform approach that focuses on the main issues.