On some derivation mechanisms and the complexity of their Szilard languages

A Szilard language is a language theoretical tool used to describe the derivation process in a formal grammar or grammar system. We investigate computational resources used by (alternating) Turing machines to accept Szilard languages of Chomsky grammars, regulated grammars and grammar systems. The results are related to the circuit complexity classes NC1 and NC2. The paper is a survey of the most important complexity results in the field, but it also brings several new insights into the parallel complexity of Szilard languages of grammar systems. We focus on parallel communicating grammar systems (PCGSs) with context-free components, and we prove that the class of Szilard languages of centralized (returning or non-returning) PCGSs is included in NC1.

[1]  Jürgen Dassow,et al.  On Cooperating Distributed Grammar Systems with Competence Based Start and Stop Conditions , 2007, Fundam. Informaticae.

[2]  Erkki Mäkinen.  On Certain Properties of Left Szilard Languages , 1983, J. Inf. Process. Cybern..

[3]  Sigrid Ewert,et al.  A shrinking lemma for random forbidding context languages , 2000, Theor. Comput. Sci..

[4]  Y. IGARASHI.  The Tape Complexity of Some Classes of Szilard Languages , 1977, SIAM J. Comput..

[5]  Erzsébet Csuhaj-Varjú,et al.  Some New Modes of Competence-Based Derivations in CD Grammar Systems , 2008, Developments in Language Theory.

[6]  Henning Fernau,et al.  On the Leftmost Derivation in Matrix Grammars , 1999, Int. J. Found. Comput. Sci..

[7]  Erzsébet Csuhaj-Varjú,et al.  On Cooperating/Distributed Grammar Systems , 1990, J. Inf. Process. Cybern..

[8]  Erkki Mäkinen,et al.  Classes of Szilard Languages in NC^1 , 2009, 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.

[9]  Erkki Mäkinen,et al.  On the Complexity of Szilard Languages of Regulated Grammars , 2011, ICTAC.

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

[11]  Arnold L. Rosenberg,et al.  Counter machines and counter languages , 1968, Mathematical systems theory.

[12]  Valeria Mihalache.  Szilard Languages Associated to Parallel Communicating Grammar Systems , 1995, Developments in Language Theory.

[13]  Penny Nii.  The blackboard model of problem solving , 1986 .

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

[15]  Martti Penttonen.  On derivation languages corresponding to context-free grammars , 2004, Acta Informatica.

[16]  Gheorghe Păun.  Parallel communication grammar systems: recent results, open problems , 1996 .

[17]  Walter L. Ruzzo.  On Uniform Circuit Complexity , 1981, J. Comput. Syst. Sci..

[18]  Martti Penttonen.  Szilard Languages are log n Tape Recognizable , 1977, J. Inf. Process. Cybern..

[19]  Gheorghe Paun.  On Szilard's Languages Associated to a Matrix Grammar , 1979, Inf. Process. Lett..

[20]  Gheorghe Paun,et al.  Grammars with Controlled Derivations , 1997, Handbook of Formal Languages.

[21]  Rainer Parchmann,et al.  Szilard Languages of IO-Grammars , 1979, Inf. Control..

[22]  Daniel J. Rosenkrantz,et al.  Programmed Grammars and Classes of Formal Languages , 1969, JACM.

[23]  S. ABRAHAM,et al.  SOME QUESTIONS OF PHRASE STRUCTURE GRAMMARS, I , 1967 .

[24]  Armin B. Cremers,et al.  A Note on Leftmost Restricted Random Context Grammars , 1973, Inf. Process. Lett..

[25]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[26]  E. Mäkinen.  A note on depth-first derivations , 1985 .

[27]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

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

[29]  Daniel J. Rosenkrantz,et al.  Programmed Grammars: A New Device for Generating Formal Languages , 1967, SWAT.

[30]  José L. Balcázar,et al.  Structural complexity 2 , 1990 .

[31]  Erkki Mäkinen,et al.  The Complexity of Szilard Languages of Matrix Grammars Revisited , 2013, Fundam. Informaticae.

[32]  Ferucio Laurentiu Tiplea,et al.  Some Decision Problems for Parallel Communicating Grammar Systems , 1994, Theor. Comput. Sci..

[33]  Heribert Vollmer,et al.  Introduction to Circuit Complexity: A Uniform Approach , 2010 .

[34]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[35]  Erkki Mäkinen.  On homomorphic images of szilard languages , 1986 .

[36]  Andries P. J. van der Walt.  Random Context Languages , 1971, IFIP Congress.

[37]  Erkki Mäkinen.  On context-free and Szilard languages , 1984, BIT Comput. Sci. Sect..

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

[39]  Henning Fernau.  Regulated Grammars under Leftmost Derivation , 2000, Grammars.

[40]  Erkki Mäkinen,et al.  On homomorphic images of left szilard languages , 1992 .

[41]  Brink van der Merwe,et al.  Bag Context Tree Grammars , 2006, Fundam. Informaticae.

[42]  Arto Salomaa,et al.  Matrix Grammars with a Leftmost Restriction , 1972, Inf. Control..

[43]  Erzsébet Csuhaj-Varjú,et al.  On Competence in CD Grammar Systems , 2004, Developments in Language Theory.

[44]  Sigrid Ewert,et al.  A pumping lemma for random permitting context languages , 2002, Theor. Comput. Sci..

[45]  Erkki Mäkinen,et al.  On the Complexity of Szilard Languages of Matrix Grammars , 2011, 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.