Deciding LTL over Mazurkiewicz traces

Abstract

Linear temporal logic (LTL) has become a well established tool for specifying the dynamic behaviour of reactive systems with an interleaving semantics, and the automata–theoretic approach has proven to be a very useful mechanism for performing automatic verification in this setting. Especially alternating automata turned out to be a powerful tool in constructing efficient yet simple to understand decision procedures and directly yield further on-the-fly model checking procedures. In this paper, we exhibit a decision procedure for LTL over Mazurkiewicz traces that generalises the classical automata–theoretic approach to a LTL interpreted no longer over sequences but certain partial orders. Specifically, we construct a (linear) alternating Büchi automaton (ABA) accepting the set of linearisations of traces satisfying the formula at hand. The salient point of our technique is to apply a notion of independence-rewriting to formulas of the logic. Furthermore, we show that the class of linear and trace-consistent ABA corresponds exactly to LTL formulas over Mazurkiewicz traces, lifting a similar result from Löding and Thomas formulated in the framework of LTL over words.