The equivalence of mappings on languages

We define the notion of the equivalence of mappings on languages in three different ways and call them universal equivalence, existential equivalence and equivalence with multiplicities. We survey recent results on this topic, as well as state some open problems.

[1]  Grzegorz Rozenberg,et al.  The mathematical theory of L systems , 1980 .

[2]  Oscar H. Ibarra,et al.  The unsolvability of the equivalence problem for e-free NGSM's with unary input (output) alphabet and applications , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[3]  Juhani Karhumäki,et al.  A Simple Undecidable Problem: Existential Agreement of Inverses of Two Morphisms on a Regular Language , 1986, J. Comput. Syst. Sci..

[4]  A. Church.  Edward F. Moore. Gedanken-experiments on sequential machines. Automata studies , edited by C. E. Shannon and J. McCarthy, Annals of Mathematics studies no. 34, litho-printed, Princeton University Press, Princeton1956, pp. 129–153. , 1958, Journal of Symbolic Logic.

[5]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[6]  Edward F. Moore,et al.  Gedanken-Experiments on Sequential Machines , 1956 .

[7]  Meera Blattner.  Single-Valued a-Transducers , 1977, J. Comput. Syst. Sci..

[8]  György E. Révész.  Introduction to formal languages , 1983 .

[9]  Juhani Karhumäki,et al.  On the Equivalence of Compositions of Morphisms and Inverse Morphisms on Regular Languages , 1985, RAIRO Theor. Informatics Appl..

[10]  Arto Salomaa,et al.  Automata-Theoretic Aspects of Formal Power Series , 1978, Texts and Monographs in Computer Science.

[11]  Karel Culik,et al.  The Decidability of the Equivalence Problem for DOL-Systems , 1977, Inf. Control..

[12]  Karel Culik,et al.  The Equivalence of Finite Valued Transducers (on HDTOL Languages) is Decidable , 1986, MFCS.

[13]  Malcolm Bird,et al.  The Equivalence Problem for Deterministic Two-Tape Automata , 1973, J. Comput. Syst. Sci..

[14]  Tom Head,et al.  The Decidability of Equivalence for Deterministic Finite Transducers , 1979, J. Comput. Syst. Sci..

[15]  G. Makanin.  The Problem of Solvability of Equations in a Free Semigroup , 1977 .

[16]  Stephen S. Yau,et al.  Two-Way Sequential Transductions and Stack Automata , 1971, Inf. Control..

[17]  K. Culík,et al.  A New Proof for the Dol Sequence Equivalence Problem and its Implications , 1986 .

[18]  Juhani Karhumäki,et al.  A note on morphic characterization of languages , 1983, Discret. Appl. Math..

[19]  Michael H. Albert,et al.  Test Sets for Finite Substitutions , 1986, Theor. Comput. Sci..

[20]  Eitan M. Gurari.  Two-way counter machines and finite-state transducers† , 1985 .

[21]  Juhani Karhumäki,et al.  The Ehrenfeucht Conjecutre: A Compactness Claim for Finitely Generated Free Monoids , 1984, Theor. Comput. Sci..

[22]  Michael H. Albert,et al.  A Proof of Ehrenfeucht's Conjecture , 1985, Theor. Comput. Sci..

[23]  On the Equivalence Problem of Compositions of Morphisms and Inverse Morphisms on Context-Free Languages , 1985, Theor. Comput. Sci..

[24]  Karel Culik,et al.  The Equivalence Problem for Single-Valued Two-Way Transducers (on NPDT0L Languages) is Decidable , 1987, SIAM J. Comput..

[25]  Arto Salomaa,et al.  On the Decidability of Homomorphism Equivalence for Languages , 1978, J. Comput. Syst. Sci..

[26]  Oscar H. Ibarra.  2DST Mapppings on Languages and Related Problems , 1982, Theor. Comput. Sci..

[27]  Timothy V. Griffiths.  The unsolvability of the Equivalence Problem for Λ-Free nondeterministic generalized machines , 1968, JACM.

[28]  Arnold L. Rosenberg,et al.  Multitape One-Way Nonwriting Automata , 1968, J. Comput. Syst. Sci..

[29]  Eitan M. Gurari.  The Equivalence Problem for Deterministic Two-Way Sequential Transducers is Decidable , 1982, SIAM J. Comput..

[30]  Karel Culik,et al.  Test Sets for Context Free Languages and Algebraic Systems of Equations over a Free Monoid , 1982, Inf. Control..

[31]  Neil D. Jones,et al.  Complete problems for deterministic polynomial time , 1974, Symposium on the Theory of Computing.

[32]  Oscar H. Ibarra.  The Unsolvability of the Equivalence Problem for epsilon-Free NGSM's with Unary Input (Output) Alphabet and Applications , 1978, SIAM J. Comput..