Inductive bases and their application to searches for minimal unary NFAs

Authors:
Geoffrey Smith
Affiliations:
Florida International University, Miami, FL
Venue:
Proceedings of the 44th annual Southeast regional conference
Year:
2006

Citing 6
Cited 0

Finite automata

Handbook of theoretical computer science (vol. B)
Minimal NFA problems are hard

SIAM Journal on Computing
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation
Introduction to Algorithms

Introduction to Algorithms
Algorithms for Computing Small NFAs

MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Word problems requiring exponential time(Preliminary Report)

STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Classic results in the theory of regular languages show that the problem of converting an NFA (nondeterministic finite automaton) into a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. This paper describes work on fast search techniques for finding minimal NFAs. The foundation of our approach is a characterization theorem for NFAs: we prove that a language is recognized by an n-state NFA iff it has what we call an inductive basis of size n. Using this characterization, we develop a fast incremental search for minimal NFAs for unary languages. We study the performance of our search algorithm experimentally, showing that, as compared with exhaustive search, it cuts the search space dramatically.