On CD-systems of stateless deterministic R-automata with window size one

Here we study cooperating distributed systems (CD-systems) of restarting automata that are very restricted: they are deterministic, they cannot rewrite, but only delete symbols, they restart immediately after performing a delete operation, they are stateless, and they have a read/write window of size 1 only, that is, these are stateless deterministic R(1)-automata. We study the expressive power of these systems by relating the class of languages that they accept by mode =1 computations to other well-studied language classes, showing in particular that this class only contains semi-linear languages. Our model can be viewed as a nondeterministic finite-state acceptor with translucent letters, that is, it processes its input in a different way than the usual left-to-right order. In this way all commutative semi-linear languages, and in fact all rational trace languages, can be accepted. In addition, we investigate the closure and non-closure properties of the class of languages accepted by our model and some of its algorithmic properties.

[1]  Victor Mitrana,et al.  Multiset Automata , 2000, WMP.

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

[3]  Martin Kutrib,et al.  On Stateless Two-Pushdown Automata and Restarting Automata , 2010, Int. J. Found. Comput. Sci..

[4]  Arto Salomaa.  Jewels of formal language theory , 1981 .

[5]  Friedrich Otto,et al.  CD-Systems of Stateless Deterministic R(1)-Automata Accept All Rational Trace Languages , 2010, LATA.

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

[7]  Martin Plátek,et al.  Towards a Formal Model for Functional Generative Description: Analysis by Reduction and Restarting Automata , 2007, Prague Bull. Math. Linguistics.

[8]  Friedrich Otto,et al.  On Deterministic CD-Systems of Restarting Automata , 2009, Int. J. Found. Comput. Sci..

[9]  Friedrich Otto,et al.  Shrinking Restarting Automata , 2007, Int. J. Found. Comput. Sci..

[10]  Gheorghe Paun,et al.  Grammar Systems: A Grammatical Approach to Distribution and Cooperation , 1995, ICALP.

[11]  Martin Kutrib,et al.  On stateless deterministic restarting automata , 2009, Acta Informatica.

[12]  James M. McQuillan,et al.  Preface Program Committee Automaton Models Inspired by Peptide Computing , 2007 .

[13]  Gheorghe Paun,et al.  Regulated Rewriting in Formal Language Theory , 1989 .

[14]  Gheorghe Paun,et al.  Grammar Systems , 1997, Handbook of Formal Languages.

[15]  Friedrich Otto,et al.  Strictly Deterministic CD-Systems of Restarting Automata , 2007, FCT.

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

[17]  Friedrich Otto,et al.  On Nonforgetting Restarting Automata That Are Deterministic and/or Monotone , 2006, CSR.

[18]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

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

[20]  Friedrich Otto,et al.  Cooperating Distributed Systems of Restarting Automata , 2007, Int. J. Found. Comput. Sci..

[21]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[22]  Jean-Camille Birget,et al.  Intersection and Union of Regular Languages and State Complexity , 1992, Inf. Process. Lett..

[23]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[24]  Martin Plátek,et al.  RESTARTING AUTOMATA: MOTIVATIONS AND APPLICATIONS , 2007 .

[25]  Karel Oliva,et al.  The Computational Complexity of Rule-Based Part-of-Speech Tagging , 2003, TSD.

[26]  Friedrich Otto.  Restarting Automata and Their Relations to the Chomsky Hierarchy , 2003, Developments in Language Theory.