HOMOMORPHISMS: DECIDABILITY, EQUALITY AND TEST SETS

Publisher Summary This chapter discusses the recent results and open problems on homomorphisms on free monoids. Most of the results are decidability results. They are motivated or directly constitute problems in L-systems theory. All of the results are the basic problems about free monoids and as such are not only of purely mathematical interest but also are of fundamental interest for theoretical computer science. The chapter discusses the iterations of one or more homomorphisms—daily oral language (DOL), HDOL, and DTOL systems—and some generalizations thereof. The problem to test whether two homomorphisms agree on a given language from family L is called the homomorphic equivalence problem for L. The chapter discusses whether two given homomorphisms agree string by string on a given language and its applications to transducers. A deterministic generalized sequential mapping (dgsm) is a mapping defined by deterministic generalized sequential machine with accepting states. The decidability of homomorphic equivalence is open for all the families of languages between DOL and indexed.

[1]  Keijo Ruohonen.  On the Decidability of the OL-DOL Equivalence Problem , 1979, Inf. Control..

[2]  Grzegorz Rozenberg,et al.  The Equivalence Problem for Deterministic T0L-Systems is Undecidable , 1972, Inf. Process. Lett..

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

[4]  Keijo Ruohonen.  Zeros of Z -Rational Functions and D0L Equivalence , 1976, Theor. Comput. Sci..

[5]  Karel Culik,et al.  Homomorphism equivalence on etol languages , 1979 .

[6]  K. Cullik,et al.  A homomorphic characterization of time and space complexity classes of languages , 1980 .

[7]  Franz-Josef Brandenburg,et al.  Equality Sets and Complexity Classes , 1980, SIAM J. Comput..

[8]  Karel Čnulík.  On some families of languages related to developmental systems , 1974 .

[9]  William E. Howden.  Lindenmayer Grammars and Symbolic Testing , 1978, Inf. Process. Lett..

[10]  Andrzej Ehrenfeucht,et al.  Every Two Equivalent DOL Systems Have a Regular True Envelope ; CU-CS-116-77 , 1977 .

[11]  Imre Simon,et al.  On Finite Semigroups of Matrices , 1977, Theor. Comput. Sci..

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

[13]  Karel Culik,et al.  Interactive L Systems with Almost Interactionless Behaviour , 1979, Inf. Control..

[14]  Andrzej Ehrenfeucht,et al.  Simplifications of Homomorphisms , 1978, Inf. Control..

[15]  Joost Engelfriet,et al.  Fixed Point Languages, Equality Languages, and Representation of Recursively Enumerable Languages , 1980, JACM.

[16]  Karel Culik.  Some Decidability Results About Regular and Pushdown Translations , 1979, Inf. Process. Lett..

[17]  Arto Salomaa.  Equality sets for homomorphisms of free monoids , 1978, Acta Cybern..

[18]  Joost Engelfriet,et al.  Equality Languages and Fixed Point Languages , 1979, Inf. Control..

[19]  Karel Culik.  A Purely Homomorphic Characterization of Recursively Enumerable Sets , 1979, JACM.

[20]  Gérard Jacob,et al.  Un Algorithme Calculant le Cardinal, Fini ou Infini, des Demi-Groupes de Matrices , 1977, Theor. Comput. Sci..

[21]  Meera Blattner.  The Unsolvability of the Equality Problem for Sentential Forms of Context-Free Grammars , 1973, J. Comput. Syst. Sci..

[22]  Andrzej Ehrenfeucht,et al.  Elementary Homomorphisms and a Solution of the D0L Sequence Equivalence Problem , 1978, Theor. Comput. Sci..

[23]  Paul M. B. Vitányi,et al.  Growth of Strings in Context Dependent Lindenmayer Systems , 1974, L Systems.

[24]  Keijo Ruohonen.  The Decidability of the F0L-D0L Equivalence Problem , 1979, Inf. Process. Lett..

[25]  Mogens Nielsen,et al.  On the Decidability of Some Equivalence Problems for D0L-Systems , 1973, Inf. Control..

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

[27]  Karel Culik.  The Decidability of v-Local Catenativity and of Other Properties of D0L Systems , 1978, Inf. Process. Lett..

[28]  Karel Culik.  On the Decidability of the Sequence Equivalence Problem for D0L-Systems , 1976, Theor. Comput. Sci..

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

[30]  Franz-Josef Brandenburg,et al.  Representing Complexity Classes by Equality Sets (Preliminary Report) , 1979, ICALP.