Remarks on generalized Post Correspondence Problem
It is shown that Post Correspondence Problem remains undecidable even in the case where one of the morphisms is fixed. Accordingly the generalized PCP is undecidable even in the case where both of the morphisms are fixed, and, moreover, the cardinality of their domain alphabet is 7. In particular, GPCP(7) is undecidable. On the other hand, GPCP(2) is not only decidable, but, as we show here, its all solutions can be effectively found.
Unable to display preview. Download preview PDF.
- 1.C. Choffrut and J. Karhumäki, Test sets for morphisms with bounded delay, Discrete Appl. Math. 12 (1985), 93–101.Google Scholar
- 2.V. Claus, Some remarks on PCP(k) and related problems, Bull. EATCS 12 (1980), 54–61.Google Scholar
- 3.K. Culik II and J. Karhumäki, On the equality sets for homomorphisms on free monoids with two generators, RAIRO Theoret. Informatics 14 (1980), 349–369.Google Scholar
- 6.S. Eilenberg, Automata, Languages, and Machines, Vol. A, Academic Press, New York, 1974.Google Scholar
- 7.M. Jantzen, “Confluent String Rewriting”, Springer-Verlag, 1988.Google Scholar
- 8.A.A. Markov, On the impossibility of certain algorithms in the theory of associative systems, Dokl. Acad. Nauk. 55 (1947), 353–356 (Russian).Google Scholar
- 9.J. Matijacevic, Simple examples of usolvable associative calculi, Dokl. Akad. Nauk 173 (1967), 1264–1266 (Russian).Google Scholar
- 11.V.A. Pavlenko, Post combinatorial problem with two pairs of words, Dokl. Akad. Nauk. Ukr. SSR (1981), 9–11.Google Scholar
- 12.E. Post, A variant of a recursively unsolvable problem, Bulletin of Amer. Math. Soc. 52 (1946), 264–268.Google Scholar
- 13.E. Post, Recursive unsolvability of a problem of Thue, J. Symb. Logic 12 (1947), 1–11.Google Scholar
- 14.K. Ruohonen, Reversible machines and Post's correspondence problem for biprefix morphisms, J. Inform. Process. Cybernet. EIK 21 (1985), 579–595.Google Scholar
- 15.G.C. Tzeitin, Associative calculus with an unsolvable equivalence problem, Tr. Mat. Inst. Akad. Nauk 52 (1958), 172–189 (Russian).Google Scholar