Locality Testing for NFAs is PSPACE-complete
Antoine Amarilli, Mika\"el Monet, R\'emi De Pretto
TL;DR
This paper proves that deciding whether an NFA recognizes a local language is PSPACE-complete, highlighting a significant computational complexity difference from the polynomial-time solvable case for DFAs.
Contribution
It establishes the PSPACE-completeness of locality testing for NFAs, contrasting with the known polynomial-time complexity for deterministic automata.
Findings
Locality testing for NFAs is PSPACE-complete.
Deterministic automata locality testing is in PTIME.
Complexity jump from DFA to NFA for locality testing.
Abstract
The class of local languages is a well-known subclass of the regular languages that admits many equivalent characterizations. In this short note we establish the PSPACE-completeness of the problem of determining, given as input a nondeterministic finite automaton (NFA) A, whether the language recognized by A is local or not. This contrasts with the case of deterministic finite automata (DFA), for which the problem is known to be in PTIME.
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Taxonomy
Topicssemigroups and automata theory · Formal Methods in Verification · Machine Learning and Algorithms