×

Multigenerative grammar systems and matrix grammars. (English) Zbl 1209.68289

Summary: Multigenerative grammar systems are based on cooperating context-free grammatical components that simultaneously generate their strings in a rule-controlled or nonterminal-controlled rewriting way, and after this simultaneous generation is completed, all the generated terminal strings are combined together by some common string operations, such as concatenation, and placed into the generated languages of these systems. The present paper proves that these systems are equivalent with the matrix grammars. In addition, we demonstrate that these systems with any number of grammatical components can be transformed to equivalent two-component versions of these systems. The paper points out that if these systems work in the leftmost rewriting way, they are more powerful than the systems working in a general way.

MSC:

68Q42 Grammars and rewriting systems
68Q45 Formal languages and automata
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[1] E. Csuhaj-Varju, J. Dassow, J. Kelemen, and Ch. Păun: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Gordon and Breach, London 1994. · Zbl 0925.68286
[2] E. Csuhaj-Varju and G. Vaszil: On context-free parallel communicating grammar systems: Synchronization, communication, and normal forms. Theoret. Comput. Sci. 255 (2001), 511-538. · Zbl 0973.68096 · doi:10.1016/S0304-3975(99)00318-7
[3] E. Csuhaj-Varju and G. Vaszil: Parallel communicating grammar systems with incomplete information communication. Develop. Language Theory (2001), 381-392.
[4] J. Dassow: On cooperating distributed grammar systems with competence based start and stop conditions. Fund. Inform. 76 (2007), 293-304. · Zbl 1112.68074
[5] J. Dassow and G. Păun: Regulated Rewriting in Formal Language Theory. Springer-Verlag, New York 1989.
[6] J. Dassow, G. Păun, and G. Rozenberg: Grammar systems. Handbook of Formal Languages (G. Rozenberg and A. Salomaa, Springer, Berlin 1997.
[7] J. Dassow, G. Păun, and A. Salomaa: Grammars with controlled derivations. Handbook of Formal Languages (G. Rozenberg and A. Salomaa, Springer, Berlin (1997).
[8] H. Fernau: Parallel communicating grammar systems with terminal transmission. Acta Inform. 37 (2001), 511-540. · Zbl 0977.68050 · doi:10.1007/PL00013312
[9] H. Fernau and M. Holzer: Graph-controlled cooperating distributed grammar systems with singleton components. Proc. Third Internat. Workshop on Descriptional Complexity of Automata, Grammars, and Related Structures, Vienna 2001, pp. 79-90. · Zbl 1095.68600
[10] J. Gaso and M. Nehez: Stochastic cooperative distributed grammar systems and random graphs. Acta Inform. 39 (2003), 119-140.
[11] M. A. Harrison: Introduction to Formal Language Theory. Addison-Wesley, London 1978. · Zbl 0411.68058
[12] A. Meduna: Automata and Languages: Theory and Applications. Springer, London 2000. · Zbl 0951.68056
[13] A. Meduna: Two-way metalinear PC grammar systems and their descriptional complexity. Acta Cybernet. 16 (2003), 126-137. · Zbl 1060.68055
[14] A. Meduna and R. Lukas: Multigenerative grammar systems. Schedae Inform. 15 (2006), 175-188.
[15] G. Păun, A. Salomaa, and S. Vicolov: On the generative capacity of parallel communicating grammar systems. Internat. J. Comput. Math. 45 (1992), 45-59. · Zbl 0796.68137 · doi:10.1080/00207169208804117
[16] G. Rozenberg and A. Salomaa: Handbook of Formal Languages. Springer, Berlin 1997. · Zbl 0866.68057
[17] A. Salomaa: Formal Languages. Academic Press, New York 1973. · Zbl 0895.00028
[18] G. Vaszil: On simulating non-returning PC grammar systems with returning systems. Theoret. Comput. Sci. 209 (1998), 1-2, 319-329. · Zbl 0915.68106 · doi:10.1016/S0304-3975(97)00120-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.