Complexity of the emptiness problem for graph-walking automata and for tilings with star subgraphs

TL;DR

This paper investigates the computational complexity of the emptiness problem for graph recognition models, establishing decidability and precise complexity bounds for graph-walking automata and star automata.

Contribution

It proves the decidability of the emptiness problem for both models and determines their complexity classes, NEXP-complete for graph-walking automata and NP-complete for star automata.

Findings

Non-emptiness for graph-walking automata is NEXP-complete.

Non-emptiness for star automata is NP-complete.

Emptiness problems are decidable for both models.

Abstract

This paper proves the decidability of the emptiness problem for two models which recognize graphs: graph-walking automata, and tilings of graphs by star subgraphs (star automata). Furthermore, it is proved that the non-emptiness problem for graph-walking automata (that is, whether a given automaton accepts at least one graph) is NEXP-complete. For star automata, which generalize nondeterministic tree automata to the case of graphs, it is proved that their non-emptiness problem is NP-complete.