On complexity of regular realizability problems
Mikhail N. Vyalyi
TL;DR
This paper investigates the computational complexity of regular realizability problems, showing their equivalence to arbitrary languages and establishing the existence of complete problems at every level of the polynomial hierarchy.
Contribution
It proves that RR problems can represent any language under disjunctive reductions and that complete RR problems exist across all polynomial hierarchy levels.
Findings
RR problems are equivalent to any language via disjunctive reductions
Complete RR problems exist at every polynomial hierarchy level
RR problems can model complex language classes
Abstract
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem equivalent to L under disjunctive reductions on nondeterministic log space. It implies that for any level of polynomial hierarchy there exists complete RR problem under polynomial reductions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Machine Learning and Algorithms · Complexity and Algorithms in Graphs