Contextual array grammars with matrix control, regular control languages, and tissue P systems control

We consider d-dimensional contextual array grammars and investigate their computational power when using various control mechanisms – matrices, regular control languages, and tissue P systems, which work like regular control languages, but may end up with a final check for the non-applicability of some rules. For d≥2, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. The use of tissue P systems with their final non-applicability check even yields some additional computational power. In the 1-dimensional case, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages can be characterized as the family of array images of the linear languages, which for a one-letter alphabet means that it coincides with the family of regular 1-dimensional array languages.

[1]  Rudolf Freund,et al.  A General Framework for Regulated Rewriting Based on the Applicability of Rules , 2011, Computation, Cooperation, and Life.

[2]  Yasunori Yamamoto,et al.  Context-sensitivity of Two-Dimensional Regular Array Grammars , 1989, Int. J. Pattern Recognit. Artif. Intell..

[3]  Rudolf Freund,et al.  Non-isometric Contextual Array Grammars with Regular Control and Local Selectors , 2015, MCU.

[4]  Marek Chrobak,et al.  Finite Automata and Unary Languages , 1986, Theor. Comput. Sci..

[5]  Rudolf Freund,et al.  Contextual Array Grammars , 2007, Formal Models, Languages and Applications.

[6]  Antonio Restivo,et al.  Two-Dimensional Languages , 1997, Handbook of Formal Languages.

[7]  Solomon Marcus,et al.  Contextual Grammars , 1969, COLING.

[8]  Rudolf Freund,et al.  Bounded Parallelism in Array Grammars Used for Character Recognition , 1996, SSPR.

[9]  Matteo Pradella,et al.  A unifying approach to picture grammars , 2009, Inf. Comput..

[10]  Gheorghe Paun,et al.  Marcus Contextual Grammars , 1994, Bull. EATCS.

[11]  K. G. Subramanian,et al.  A note on regular-controlled apical-growth filamentous systems , 1985, International Journal of Computer & Information Sciences.

[12]  Benedek Nagy.  On a hierarchy of 5′ → 3′ sensing Watson-Crick finite automata languages , 2013, J. Log. Comput..

[13]  Patrick Shen-Pei Wang,et al.  Some New Results on Isotonic Array Grammars , 1980, Inf. Process. Lett..

[14]  Azriel Rosenfeld,et al.  Picture languages—a survey , 1993 .

[15]  Gheorghe Paun,et al.  The Oxford Handbook of Membrane Computing , 2010 .

[16]  Raghavan Rama,et al.  Array Contextual Grammars , 2000, Recent Topics in Mathematical and Computational Linguistics.

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

[18]  Rudolf Freund.  Control Mechanisms on #-Context-Free Array Grammars , 1994, Mathematical Aspects of Natural and Formal Languages.

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

[20]  Rudolf Freund,et al.  Contextual Array Grammars with Matrix and Regular Control , 2016, DCFS.