On the Complexity of Szilard Languages of Matrix Grammars

We investigate computational resources used by alternating Turing machines (ATMs) to accept Szilard languages (SZLs) of context-free matrix grammars (MGs). The main goal is to relate these languages to parallel complexity classes such as NC1 and NC2. We prove that unrestricted and leftmost-1 SZLs of context-free MGs, without appearance checking, can be accepted by ATMs in logarithmic time and space. Hence, these classes of languages belong to NC1 (under ALOGTIME reduction). Unrestricted SZLs of context-free MGs with appearance checking can be accepted by ATMs in logarithmic space and square logarithmic time. Consequently, this class is contained in NC2. We conclude with some results on SZLs of MGs with phrase-structure rules.

[1]  Erkki Mäkinen.  On Szilard Languages of Pure Context-free Grammars , 1986, J. Inf. Process. Cybern..

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

[3]  Ryan Williams,et al.  Uniform Circuit Complexity , 2013 .

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

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

[7]  Etsuro Moriya,et al.  Associate Languages and Derivational Complexity of Formal Grammars and Languages , 1973, Inf. Control..

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

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

[10]  Arthur C. Fleck.  An Analysis of Grammars by Their Derivation Sets , 1974, Inf. Control..

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

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

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

[14]  José L. Balcázar,et al.  Structural Complexity II , 2012, EATCS.

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

[16]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

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

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

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

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