On product hierarchies of automata

P. Dömösi, Z. Ésik, B. Imreh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We have seen that, with respect to homomorphic realization, the νi—products behave in a way similar to the αi—products on classes satisfying the Letičevskiî criterion or not satisfying the Letičevskiî criteria. In particular, a class K is homomorphically ν3—complete if and only if it satisfies the Letičevskiî criterion. As opposed to the αi—products, the νi—hierarchy is proper on classes with the semi-Letičevskiî criterion. This holds also for homomorphic realization. To give a summary of the rest of our comparison results, take any two of our product notions, the “β—product” and the “γ—product”, say. Define γ if holds for all K. Similarly let γ if we have for all K. We obtain two poset structures whose exact diagrams are given in the figures below. The bottom is the quasi-direct product in both cases, for it is obvious that and ν1, henceforth also and. (We write β<γ if β≤γ but γ≰β.) Recently it has been shown by the first two authors that there is a class K satisfying the Letičevskiî criterion but which is not homomorphically ν2-complete.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - International Conference, FCT 1989, Proceedings
PublisherSpringer Verlag
Pages137-144
Number of pages8
ISBN (Print)9783540514985
DOIs
Publication statusPublished - Jan 1 1989
Event7th International Conference on Fundamentals of Computation Theory, FCT 1989 - Szeged, Hungary
Duration: Aug 21 1989Aug 25 1989

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume380 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Fundamentals of Computation Theory, FCT 1989
CountryHungary
CitySzeged
Period8/21/898/25/89

Fingerprint

Automata
Homomorphic
Comparison Result
Direct Product
Poset
Figure
Diagram
Hierarchy
If and only if
Class

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Dömösi, P., Ésik, Z., & Imreh, B. (1989). On product hierarchies of automata. In Fundamentals of Computation Theory - International Conference, FCT 1989, Proceedings (pp. 137-144). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 380 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-51498-8_13

On product hierarchies of automata. / Dömösi, P.; Ésik, Z.; Imreh, B.

Fundamentals of Computation Theory - International Conference, FCT 1989, Proceedings. Springer Verlag, 1989. p. 137-144 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 380 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dömösi, P, Ésik, Z & Imreh, B 1989, On product hierarchies of automata. in Fundamentals of Computation Theory - International Conference, FCT 1989, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 380 LNCS, Springer Verlag, pp. 137-144, 7th International Conference on Fundamentals of Computation Theory, FCT 1989, Szeged, Hungary, 8/21/89. https://doi.org/10.1007/3-540-51498-8_13
Dömösi P, Ésik Z, Imreh B. On product hierarchies of automata. In Fundamentals of Computation Theory - International Conference, FCT 1989, Proceedings. Springer Verlag. 1989. p. 137-144. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-51498-8_13
Dömösi, P. ; Ésik, Z. ; Imreh, B. / On product hierarchies of automata. Fundamentals of Computation Theory - International Conference, FCT 1989, Proceedings. Springer Verlag, 1989. pp. 137-144 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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