Reachability of Communicating Timed Processes

TL;DR

This paper analyzes the reachability problem for communicating timed automata with local clocks and FIFO channels, providing a complete classification of decidability and complexity results for various topologies.

Contribution

It offers a complete characterization of decidable and undecidable communication topologies for timed automata, with complexity analysis linking to Petri nets.

Findings

Decidable and undecidable communication topologies identified.

Complexity results show equivalence to Petri nets in discrete time.

Mutual reductions between timed automata and counter automata established.

Abstract

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata.