Emptiness Problems for Distributed Automata

Antti Kuusisto
Fabian Reiter

We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite sequence of synchronous rounds. The problem is shown to be decidable in LogSpace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. When restricted to the appropriate families of graphs, these forgetful automata are equivalent to classical finite word automata, but strictly more expressive than finite tree automata. On the other hand, we also show that the emptiness problem is undecidable in general. This already holds for two heavily restricted classes of distributed automata: those that reject immediately if they receive more than one message per round, and those whose state diagram must be acyclic except for self-loops.

In Patricia Bouyer, Andrea Orlandini and Pierluigi San Pietro: Proceedings Eighth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2017), Roma, Italy, 20-22 September 2017, Electronic Proceedings in Theoretical Computer Science 256, pp. 210–222.
13 pages, 2 figures
Published: 6th September 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.256.15 bibtex PDF
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