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Emptiness problems for distributed automata

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Article number104503
JournalInformation and Computation
Publication statusE-pub ahead of print - 2019
Publication typeA1 Journal article-refereed


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. Additionally, to demonstrate the flexibility of distributed automata in simulating different models of computation, we provide a characterization of constraint satisfaction problems by identifying a class of automata with exactly the same computational power.


  • Distributed computing, Emptiness problem, Finite automata

Publication forum classification

Field of science, Statistics Finland