Restarting Automata and Their Relations to the Chomsky Hierarchy

The restarting automaton, introduced by Jancar et al in 1995, is motivated by the so-called 'analysis by reduction, ' a technique from linguistics. By now there are many different models of restarting automata, and their investigation has proved very fruitful in that they offer an opportunity to study the influence of various kinds of resources on their expressive power. Here a survey on the various models and their properties is given, their relationships to the language classes of the Chomsky hierarchy are described, and some open problems are presented.

[1]  Jens R. Woinowski.  Church-Rosser languages and their application to parsing problems , 2001 .

[2]  Friedrich Otto,et al.  Confluent Internal Contextual Languages , 2000, Recent Topics in Mathematical and Computational Linguistics.

[3]  Frantisek Mráz,et al.  Lookahead Hierarchies of Restarting Automata , 2001, J. Autom. Lang. Comb..

[4]  Krzysztof Lorys,et al.  Church-Rosser Languages vs. UCFL , 2002, ICALP.

[5]  Frantisek Mráz,et al.  On Monotonic Automata with a Restart Operation , 1999, J. Autom. Lang. Comb..

[6]  Manfred K. Warmuth,et al.  Membership for Growing Context-Sensitive Grammars is Polynomial , 1986, J. Comput. Syst. Sci..

[7]  Friedrich Otto,et al.  McNaughton families of languages , 2003, Theor. Comput. Sci..

[8]  Robert McNaughton.  An Insertion into the Chomsky Hierarchy? , 1999, Jewels are Forever.

[9]  Rohit Parikh,et al.  On Context-Free Languages , 1966, JACM.

[10]  Gundula Niemann.  Church-Rosser languages and related classes , 2003 .

[11]  Johannes Waldmann,et al.  Some Regular Languages That Are Church-Rosser Congruential , 2001, Developments in Language Theory.

[12]  Frantisek Mráz,et al.  Restarting Automata, Marcus Grammars and Context-Free Languages , 1995, Developments in Language Theory.

[13]  Frantisek Mráz,et al.  Restarting Automata, Deleting and Marcus Grammars , 2000, Recent Topics in Mathematical and Computational Linguistics.

[14]  Sebastiaan H. von Solms.  The Characterization by Automata of Certain Classes of Languages in the Context Sensititve Area , 1975, Inf. Control..

[15]  Friedrich Otto,et al.  Restarting automata, Church-Rosser languages, and representations of r.e. languages , 1999, Developments in Language Theory.

[16]  Martin Plátek,et al.  Two-Way Restarting Automata and J-Monotonicity , 2001, SOFSEM.

[17]  Friedrich Otto,et al.  On the Power of RRWW-Automata , 2001, Words, Semigroups, and Transductions.

[18]  Friedrich Otto,et al.  String-Rewriting Systems , 1993, Text and Monographs in Computer Science.

[19]  Gheorghe Paun,et al.  Contextual Grammars and Formal Languages , 1997, Handbook of Formal Languages.

[20]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[21]  Jens R. Woinowski.  A Normal Form for Church-Rosser Language Systems , 2001, RTA.

[22]  Paliath Narendran.  Church-rosser and related thue systems (word problem, rewrite rules, congruence) , 1984 .

[23]  Friedrich Otto,et al.  Infinite Convergent String-Rewriting Systems and Cross-Sections for Finitely Presented Monoids , 1998, J. Symb. Comput..

[24]  Frantisek Mráz,et al.  Different Types of Monotonicity for Restarting Automata , 1998, FSTTCS.

[25]  Friedrich Otto,et al.  The Church-Rosser Languages Are the Deterministic Variants of the Growing Context-Sensitive Languages , 1998, FoSSaCS.

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

[27]  Frantisek Mráz,et al.  Restarting Automata , 1995, FCT.

[28]  Frantisek Mráz,et al.  Monotonic Rewriting Automata with a Restart Operation , 1997, SOFSEM.

[29]  Markéta Stranáková,et al.  Selected Types of Pg-Ambiguity , 1999, Prague Bull. Math. Linguistics.

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

[31]  Gheorghe Paun,et al.  On Representing Recursively Enumerable Languages by Internal Contextual Languages , 1998, Theor. Comput. Sci..

[32]  Jens R. Woinowski,et al.  The Growing Context-Sensitive Languages Are the Acyclic Context-Sensitive Languages , 2001, Developments in Language Theory.

[33]  Frantisek Mráz,et al.  A Taxonomy of Forgetting Automata , 1993, MFCS.

[34]  Solomon Marcus,et al.  Contextual Grammars and Natural Languages , 1997, Handbook of Formal Languages.

[35]  Friedrich Otto,et al.  Further Results on Restarting Automata , 2000, Words, Languages & Combinatorics.

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

[37]  Paliath Narendran,et al.  Church-Rosser Thue systems and formal languages , 1988, JACM.

[38]  Gerhard Buntrock,et al.  Growing Context-Sensitive Languages and Church-Rosser Languages , 1998, Inf. Comput..

[39]  Martin Plátek,et al.  A note on the Chomsky hierarchy , 1985, Bull. EATCS.

[40]  Markéta Stranáková.  Selected Types of Pg-Ambiguity: Processing Based on Analysis by Reduction , 2000, TSD.