Prime languages

Orna Kupferman*, Jonathan Mosheiff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We say that a deterministic finite automaton (DFA) A is composite if there are DFAs A1,...,At such that L(A) = ∩i=1t L(Ai) and the index of every Ai is strictly smaller than the index of A. Otherwise, A is prime. We study the problem of deciding whether a given DFA is composite, the number of DFAs required in a decomposition, decompositions that are based on abstractions, methods to prove primality, and structural properties of DFAs that make the problem simpler or are retained in a decomposition. We also provide an algebraic view of the problem and demonstrate its usefulness for the special case of permutation DFAs.

Original languageAmerican English
Pages (from-to)90-107
Number of pages18
JournalInformation and Computation
StatePublished - Feb 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.


  • DFA decomposition
  • Deterministic finite automaton (DFA)
  • Prime DFA
  • Prime regular languages
  • Regular languages


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