The state complexity of random DFAs

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1 Scopus citations


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 αkn+O(nlog⁡n) for a certain explicit constant αk.

Original languageEnglish
Pages (from-to)102-108
Number of pages7
JournalTheoretical Computer Science
StatePublished - 1 Nov 2016


  • DFA
  • Deterministic finite-state automaton
  • Minimal
  • Random

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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