Lower bounds for the transition complexity of NFAs

Authors:
Michael Domaratzki;Kai Salomaa
Affiliations:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba R3T 2T2, Canada;School of Computing, Queen's University, Kingston, Ontario K7L 3N6, Canada
Venue:
Journal of Computer and System Sciences
Year:
2008

Citing 19
Cited 4

Minimal NFA problems are hard

SIAM Journal on Computing
A lower bound technique for the size of nondeterministic finite automata

Information Processing Letters
Communication complexity and parallel computing

Communication complexity and parallel computing
Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata

SIAM Journal on Computing
State complexity of regular languages

Journal of Automata, Languages and Combinatorics
Translating regular expressions into small εe-free nondeterministic finite automata

Journal of Computer and System Sciences
A lower bound on the size of ɛ-free NFA corresponding to a regular expression

Information Processing Letters
Descriptional complexity of finite automata: concepts and open problems

Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Minimizing finite automata is computationally hard

Theoretical Computer Science - Developments in language theory
Comparing the size of NFAs with and without ε-transitions

Theoretical Computer Science
Minimizing nfa's and regular expressions

Journal of Computer and System Sciences
Transition complexity of language operations

Theoretical Computer Science
On the average state and transition complexity of finite languages

Theoretical Computer Science
Unary language operations and their nondeterministic state complexity

DLT'02 Proceedings of the 6th international conference on Developments in language theory
Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP

DLT'07 Proceedings of the 11th international conference on Developments in language theory
Extremal Combinatorics: With Applications in Computer Science

Extremal Combinatorics: With Applications in Computer Science
Regular expressions and NFAs without Ε-transitions

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Lower bounds for the transition complexity of NFAs

MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Finding lower bounds for nondeterministic state complexity is hard

DLT'06 Proceedings of the 10th international conference on Developments in Language Theory

State Complexity of Nested Word Automata

LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Nondeterministic state complexity of nested word automata

Theoretical Computer Science
Limitations of lower bound methods for deterministic nested word automata

Information and Computation
Transition Complexity of Incomplete DFAs

Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday

Quantified Score

Hi-index	0.00

Visualization

Abstract

We construct regular languages L"n, n=1, such that any NFA recognizing L"n needs @W(nsc(L"n)@?nsc(L"n)) transitions. Here nsc(L"n) is the nondeterministic state complexity of L"n. Also, we study trade-offs between the number of states and the number of transitions of an NFA. We show that adding one additional state can result in significant reductions in the number of transitions and that there exist regular languages L"n, n=2, where the transition minimal NFA for L"n has more than c@?nsc(L"n) states, for some constant c1.