Critical classes for the α0-product

Pál Dömösi, Zoltán Ésik

Research output: Contribution to journalArticle

4 Citations (Scopus)


The Krohn-Rhodes Decomposition Theorem provides two necessary conditions as regards (homomorphic) completeness for the α0-product. We call a class K0 of automata critical if, for every class K, the above necessary conditions and the inclusion K0 ⊆ HSPα0(K) jointly imply that K is complete for the α0-product. We proved that the class K0 consisting of all counters and the two-state reset automation is critical. Here we describe all critical classes.

Original languageEnglish
Pages (from-to)17-24
Number of pages8
JournalTheoretical Computer Science
Issue number1
Publication statusPublished - Oct 1988

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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