Homomorphisms Preserving Deterministic Context-Free Languages

The paper characterizes the family of homomorphisms, under which the deterministic context-free languages, the LL context-free languages and the unambiguous context-free languages are closed. The family of deterministic context-free languages is closed under a homomorphism h if and only if h is either a code of bounded deciphering delay, or the images of all symbols under h are powers of the same string. The same characterization holds for LL context-free languages. The unambiguous context-free languages are closed under h if and only if either h is a code, or the images of all symbols under h are powers of the same string.

[1]  Alexander Okhotin,et al.  Boolean Grammars and GSM Mappings , 2010, Int. J. Found. Comput. Sci..

[2]  Alexander Okhotin.  Homomorphisms Preserving Linear Conjunctive Languages , 2008, J. Autom. Lang. Comb..

[3]  M. Lothaire.  Combinatorics on words: Bibliography , 1997 .

[4]  Vèronique Bruyère.  Maximal Codes With Bounded Deciphering Delay , 1991, Theor. Comput. Sci..

[5]  Ludwig Staiger,et al.  On Infinitary Finite Length Codes , 1986, RAIRO Theor. Informatics Appl..

[6]  Noam Chomsky,et al.  The Algebraic Theory of Context-Free Languages* , 1963 .

[7]  Jean Berstel,et al.  Context-Free Languages and Pushdown Automata , 1997, Handbook of Formal Languages.

[8]  Alexander Okhotin,et al.  On the equivalence of linear conjunctive grammars and trellis automata , 2004, RAIRO Theor. Informatics Appl..

[9]  Seymour Ginsburg,et al.  Deterministic Context Free Languages , 1966, Inf. Control..

[10]  Derick Wood.  A Further Note on Top-Down Deterministic Languages , 1971, Comput. J..

[11]  M. P. Schützenberger.  On a question concerning certain free submonoids , 1966 .

[12]  Dominique Perrin,et al.  Codes and Automata , 2009, Encyclopedia of mathematics and its applications.

[13]  Joseph S. Ullian,et al.  Preservation of unambiguity and inherent ambiguity in context-free languages , 1966, JACM.

[14]  Daniel J. Rosenkrantz,et al.  Properties of Deterministic Top-Down Grammars , 1970, Inf. Control..

[15]  Antonio Restivo,et al.  A Combinatorial Property of Codes Having Finite Synchronization Delay , 1975, Theor. Comput. Sci..