Transducers and the Decidability of Independence in Free Monoids

Abstract A transducer-based general method is derived by which proofs of the decidability of independence of regular languages with respect to a given relation can be obtained. This permits a uniform proof of the decidability of certain code properties which so far has only been obtained using separate, quite different and ad hoc proofs.

[1]  Helmut Jürgensen,et al.  n-Prefix–suffix languages ∗ , 1989 .

[2]  Helmut Jürgensen,et al.  Languages Whose n-Element Subsets Are Codes , 1992, Theor. Comput. Sci..

[3]  Seymour Ginsburg,et al.  Preservation of Languages by Transducers , 1966, Inf. Control..

[4]  Joost Engelfriet,et al.  Pushdown Machines for the Macro Tree Transducer , 1986, Theor. Comput. Sci..

[5]  Helmut Jürgensen,et al.  Solid Codes , 1991, J. Inf. Process. Cybern..

[6]  Werner Damm,et al.  An Automata-Theoretical Characterization of the OI-Hierarchy , 1986, Inf. Control..

[7]  Stavros Konstantinidis,et al.  The Hierarchy of Codes , 1993, FCT.

[8]  Joost Engelfriet,et al.  IO and OI. I , 1977, J. Comput. Syst. Sci..

[9]  Masami Ito,et al.  Anti-commutative languages and n-codes , 1989, Discret. Appl. Math..

[10]  Alfred V. Aho Indexed Grammars-An Extension of Context Free Grammars , 1967, SWAT.

[11]  Sheila A. Greibach,et al.  Checking Automata and One-Way Stack Languages , 1969, J. Comput. Syst. Sci..

[12]  Joost Engelfriet,et al.  Pushdown machines for the macro tree transducer: theoretical computer sciences 42(3) (1986) 251-368 , 1986 .

[13]  Joost Engelfriet,et al.  Iterated Stack Automata and Complexity Classes , 1991, Inf. Comput..

[14]  Sheng Yu,et al.  Decidability of the Intercode Property , 1993, J. Inf. Process. Cybern..

[15]  Sheila A. Greibach Full AFLs and Nested Iterated Substitution , 1970, Inf. Control..

[16]  Oscar H. Ibarra,et al.  Reversal-Bounded Multicounter Machines and Their Decision Problems , 1978, JACM.

[17]  Werner Damm,et al.  The IO- and OI-Hierarchies , 1982, Theor. Comput. Sci..

[18]  M. Schützenberger,et al.  The equation $a^M=b^Nc^P$ in a free group. , 1962 .

[19]  J. Engelfriet,et al.  IO and OI , 1975 .

[20]  Joost Engelfriet,et al.  Look-Ahead on Pushdowns , 1987, Inf. Comput..

[21]  J. Berstel,et al.  Theory of codes , 1985 .

[22]  Tom Head,et al.  Deciding Code Related Properties by Means of Finite Transducers , 1993 .

[23]  Helmut Jürgensen,et al.  Relations on free monoids, their independent sets, and codes , 1991, Int. J. Comput. Math..