Summary
Equivalence problems of some transductions involving letter to letter morphisms on regular languages are discussed. In particular, we deal with finite substitutions and inverses of finite substitutions. Our main results are the following: (i) The equivalence problem of inverses of finite substitutions on regular languages is undecidable, (ii) The existential equivalence problem of finite substitutions on regular languages is undecidable, and (iii) The length-equivalence problem of finite substitutions on regular languages is decidable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albert, J., Culik, K.II, Karhumäki, J.: Test sets for context-free languages and algebraic systems of equations. Information and Control 52, 172–186 (1982)
Berstel, J.: Transductions and Context-Free Languages. Stuttgart: Teubner 1979
Blattner, M., Head, T.: Single-Valued a-Transducers. JCSS 15, 310–327 (1977)
Culik, K.II: Some decidability results about regular and pushdown translations. Information Processing Letters 8, 5–8 (1979)
Culik, K.II, Karhumäki, J.: Systems of equations over a free monoid and Ehrenfeucht's Conjecture. Discrete Mathematics 43, 139–153 (1983)
Culik, K.II, Salomaa, A.: On the decidability of homomorphism equivalence for languages. JCSS 17, 163–175 (1978)
Griffiths, T.V.: The unsolvability of the equivalence problem for λ-free non-deterministic generalized machines. JACM 15, 409–413 (1968)
Harrison, M.: Introduction to Formal Language Theory. Reading, MA: Addison-Wesley 1978
Ibarra, O.H.: On some decision questions concerning pushdown machines. TCS 24, 313–322 (1983)
Ibarra, O.H.: The unsolvability of the equivalence problem for ɛ-free NGSM's with unary input (output) alphabet and applications. SIAM J. COMPUT. 7, 524–532 (1978)
Karhumäki, J.: Problems and solutions, P97. Bulletin of the EATCS 25, 184–185 (1985)
Karhumäki, J., Kleijn, H.C.M.: On the equivalence of compositions of morphisms and inverse morphisms on regular languages. Lect. Notes Comput. Sci. 176, 355–363 (1984). Also: RAIRO, Inform. Théor. (To appear)
Karhumäki, J., Maon, Y.: A simple undecidable problem: Existential agreement of inverses of two morphisms on a regular language. JCSS (To appear)
Karhumäki, J., Wood, D.: Inverse morphic equivalence on languages. Inform. Processing Letters 19, 213–218 (1984)
Maon, Y.: A note on the equivalence problem of composition of morphisms and inverse morphisms on context-free languages. Technical-Report 021/84, (1984), Dept. of Comp. Sci., Tel-Aviv University. Also TCS, (To appear)
Maon, Y.: Decision problems concerning equivalence of transductions on languages. Ph. D. Thesis, Dept. of Comp. Sci., Tel-Aviv University
Maon, Y., Yehudai, A.: Balance of many-valued transductions and equivalence problems. Technical-Report 030/85, (1985), Dept. of Comp. Sci., Tel-Aviv University (Submitted for publication)
Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. New York: Academic Press 1980
Schützenberger, M.P.: Sur les relations rationelles. In: Brakhage, H. (ed.). Automata Theory and Formal Languages, 2nd GI Conference. Lect. Notes Comput. Sci. 33, 209–213 (1975)
Turakainen, P.: A machine-oriented approach to compositions of morphisms and inverse morphisms. EATCS Bull. 20, 162–166 (1983)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maon, Y. On the equivalence of some transductions involving letter to letter morphisms on regular languages. Acta Informatica 23, 585–596 (1986). https://doi.org/10.1007/BF00288471
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00288471