Timed Systems through the Lens of Logic

TL;DR

This paper investigates the logical properties of timed systems with data structures, establishing their definability in a specific logic and introducing a new analysis technique that handles complex features efficiently.

Contribution

It proves the realizability property for timed graph collections is definable in EQ-ICPDL and introduces a novel, efficient proof technique for analyzing enriched timed systems.

Findings

Realizability property is logically definable in EQ-ICPDL.

New algorithmic technique for analyzing timed systems with data structures.

Extended analysis capabilities for systems with stacks and queues.

Abstract

In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called realizable if we can assign time-stamps to nodes or events so that they are consistent with the timing constraints. The logical definability of several graph properties has been a challenging problem, and we show, using a highly non-trivial argument, that the realizability property for collections of graphs with strict timing constraints is logically definable in a class of propositional dynamic logic (EQ-ICPDL), which is strictly contained in MSO. Using this result, we propose a novel, algorithmically efficient and uniform proof technique for the analysis of timed systems enriched with auxiliary data structures, like stacks and queues. Our technique unravels new results (for emptiness checking as well as model checking) for timed systems with richer features than considered so far, while also recovering existing results.