A Unified Automata-Theoretic Approach to LTLf Modulo Theories (Extended Version)

TL;DR

This paper introduces a new automata-based method for checking LTLf modulo theories, extending traditional LTLf with first-order formulas over various theories, and demonstrates its practical effectiveness.

Contribution

It develops a symbolic automata approach for LTL-MT, enabling applications like model checking and runtime monitoring, supported by efficient solvers.

Findings

Satisfiability checking with LTL-MT is feasible using SDWAs.

The approach performs comparably to previous solutions in empirical tests.

Reduces LTL-MT satisfiability to constrained Horn clauses for solver support.

Abstract

We present a novel automata-based approach to address linear temporal logic modulo theory (LTL-MT) as a specification language for data words. LTL-MT extends LTL_f by replacing atomic propositions with quantifier-free multi-sorted first-order formulas interpreted over arbitrary theories. While standard LTL_f is reduced to finite automata, we reduce LTL-MT to symbolic data-word automata (SDWAs), whose transitions are guarded by constraints from underlying theories. Both the satisfiability of LTL-MT and the emptiness of SDWAs are undecidable, but the latter can be reduced to a system of constrained Horn clauses, which are supported by efficient solvers and ongoing research efforts. We discuss multiple applications of our approach beyond satisfiability, including model checking and runtime monitoring. Finally, a set of empirical experiments shows that our approach to satisfiability works at least as well as a previous custom solution.