The Emptiness Problem for Tree Automata with at Least One Disequality Constraint is NP-hard
P.-C H\'eam (INRIA Nancy - Grand Est / LORIA / LIFC, FEMTO-ST), V., Hugot (INRIA Lille - Nord Europe, LIFL), O. Kouchnarenko (FEMTO-ST, INRIA, Nancy - Grand Est / LORIA / LIFC)
TL;DR
This paper proves that the emptiness problem for tree automata with at least one disequality constraint is NP-hard, highlighting computational complexity challenges in this automata model.
Contribution
It establishes NP-hardness of the emptiness problem for tree automata with disequality constraints, extending understanding of their computational complexity.
Findings
Emptiness problem is NP-hard with at least one disequality constraint.
The result applies to tree automata models introduced in 2007.
Highlights complexity challenges in automata with disequality constraints.
Abstract
The model of tree automata with equality and disequality constraints was introduced in 2007 by Filiot, Talbot and Tison. In this paper we show that if there is at least one disequality constraint, the emptiness problem is NP-hard.
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Taxonomy
Topicssemigroups and automata theory · Formal Methods in Verification · Logic, programming, and type systems