The state complexity of random DFAs

Daniel Berend; Aryeh Kontorovich

doi:10.1016/j.tcs.2016.09.012

The state complexity of random DFAs

Daniel Berend, Aryeh Kontorovich

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random n-state DFAs over a k-symbol alphabet, drawn uniformly from the set [n]^[n]×[k]×2^[n] of all such automata. We show that, with high probability, the latter is α_kn+O(nlog⁡n) for a certain explicit constant α_k.

Original language	English
Pages (from-to)	102-108
Number of pages	7
Journal	Theoretical Computer Science
Volume	652
DOIs	https://doi.org/10.1016/j.tcs.2016.09.012
State	Published - 1 Nov 2016

Keywords

DFA
Deterministic finite-state automaton
Minimal
Random

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2016.09.012

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KW - Deterministic finite-state automaton

KW - Minimal

KW - Random

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The state complexity of random DFAs

Abstract

Keywords

ASJC Scopus subject areas

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