Iterated sequential transducers as language generating devices

Iterated finite state sequential transducers are considered as language generating devices. The hierarchy induced by the size of the state alphabet is proved to collapse to the fourth level. The corresponding language families are related to the families of languages generated by Lindenmayer systems and Chomsky grammars. Finally, some results on deterministic and extended iterated finite state transducers are established.

[1]  P.R.J. Asveld On controlled iterated gsm mappings and related operations : (preprint) , 1979 .

[2]  Hideyuki Takahashi The Maximum Invariant Set of an Automaton System , 1976, Inf. Control..

[3]  Roland Vollmar Algorithmen in Zellularautomaten , 1979 .

[4]  Michel Latteux,et al.  Iterated Length-Preserving Rational Transductions , 1998, MFCS.

[5]  Wolfgang Rülling Informationsübertragung in L-Systemen , 1983 .

[6]  G. Herman Computing ability of a developmental model for filamentous organisms. , 1969, Journal of theoretical biology.

[7]  Victor Mitrana,et al.  Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology, and Back: Essays in Honour of Gheorghe Paun , 2003, Grammars and Automata for String Processing.

[8]  R. K. Shyamasundar,et al.  Programmed OL-systems , 1980, Inf. Sci..

[9]  Joaquim Gabarró,et al.  Iterated GSMs and Co-CFL , 1989, Acta Informatica.

[10]  Henning Fernau,et al.  On Iterated Sequential Transducers , 2003, Grammars and Automata for String Processing.

[11]  G. Paun,et al.  Jewels are Forever , 1999, Springer Berlin Heidelberg.

[12]  Satoshi Kobayashi Iterated Transductions and Efficient Learning from Positive Data: A Unifying View , 2000, ICGI.

[13]  Vincenzo Manca,et al.  On the Generative Power of Iterated Transductions , 2001, Words, Semigroups, and Transductions.

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

[15]  J. McCarthy,et al.  Automata Studies. (AM-34) (Annals of Mathematics Studies) , 1956 .

[16]  Grzegorz Rozenberg,et al.  Developmental systems and languages , 1972, STOC.

[17]  Gheorghe Paun,et al.  Words, Semigroups, and Transductions , 2001 .

[18]  C Martín-Vide,et al.  New computing paradigms suggested by DNA computing: computing by carving. , 1999, Bio Systems.

[19]  Henning Fernau,et al.  The degree of parallelism , 2005, DCFS.

[20]  Jürgen Dassow,et al.  Information transmission in il systems , 1990, Int. J. Comput. Math..

[21]  Carlos Martín-Vide,et al.  Iterated GSM Mappings: A Collapsing Hierarchy , 1999, Jewels are Forever.

[22]  Claude E. Shannon,et al.  A Universal Turing Machine with Two Internal States , 1956 .

[23]  Branislav Rovan A Framework for Studying Grammars , 1981, MFCS.

[24]  Derick Wood Iterated a-NGSM Maps and \Gamma Systems , 1976, Inf. Control..

[25]  Frantisek Mráz,et al.  On Restarting Automata with Rewriting , 1997, New Trends in Formal Languages.

[26]  Paul M. B. Vitányi,et al.  Lindenmayer systems: structure, languages, and growth functions , 1978 .

[27]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[28]  Dirk van Dalen A note on some systems of lindenmayer , 2005, Mathematical systems theory.

[29]  David Simplot-Ryl,et al.  Closure under union and composition of iterated rational transductions , 2000, RAIRO Theor. Informatics Appl..

[30]  Viliam Geffert Normal forms for phrase-structure grammars , 1991, RAIRO Theor. Informatics Appl..