The Myhill-Nerode Theorem for Recognizable Tree Series
- 314 Downloads
In this paper we prove a Myhill-Nerode theorem for recognizable tree series over commutative semifields and thereby present a minimization of bottom-up finite state weighted tree automata over a commutative semifield, where minimal means with respect to the number of states among all equivalent, deterministic devices.
KeywordsFormal Power Series Tree Representation Congruence Relation Tree Series Tree Automaton
Unable to display preview. Download preview PDF.
- J. Berstel and Ch. Reutenauer. Rational Series and Their Languages, volume 12 of EATCS-Monographs. Springer Verlag, 1988.Google Scholar
- B. Borchardt and H. Vogler. Determinization of Finite State Weighted Tree Automata. J. Automata, Languages and Combinatorics, accepted, 2003.Google Scholar
- M. Droste and D. Kuske. Skew and infinitary formal power series. Technical Report 2002-38, Department of Mathematics and Computer Science, University of Leicester, 2002.Google Scholar
- S. Eilenberg. Automata, Languages, and Machines, Vol.A. Academic Press, 1974.Google Scholar
- Z. Esik and W. Kuich. Formal Tree Series. J. Automata, Languages and Combinatorics, accepted, 2003.Google Scholar
- Z. Fülöp and S. Vágvölgyi. Congruential tree languages are the same as recognizable tree languages. Bulletin of EATCS, 30:175–185, 1989.Google Scholar
- Z. Fülöp and H. Vogler. Tree series transformations that respect copying. Theory of Computing Systems, to appear, 2003.Google Scholar
- F. Gécseg and M. Steinby. Tree languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 3, chapter 1, pages 1–68. Springer-Verlag, 1997.Google Scholar
- W. Kuich. Formal power series over trees. In S. Bozapalidis, editor, Proc. of the 3rd International Conference Developments in Language Theory, pages 61–101. Aristotle University of Thessaloniki, 1998.Google Scholar
- W. Kuich and A. Salomaa. Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science, Springer Verlag, 1986.Google Scholar
- M. Magidor and G. Moran. Finite automata over finite trees. Technical Report 30, Hebrew University, Jerusalem, 1969.Google Scholar