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Grammar Systems

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Handbook of Formal Languages

Abstract

In classic formal language and automata theory, grammars and automata were modeling classic computing devices. Such devices were “centralized” — the computation was accomplished by one “central” agent. Hence in classic formal language theory a language is generated by one grammar or recognized by one automaton. In modern computer science distributed computation plays major role. Analyzing such computations in computer networks, distributed data bases, etc., leads to notions such as distribution, parallelism, concurrency, and communication. The theory of grammar systems was developed as a grammatical model for distributed computation where these notions could be defined and analyzed.

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References

  1. S. Abraham, Compound and serial grammars, Inform. Control, 20 (1972), 432–438.

    MathSciNet  MATH  Google Scholar 

  2. L. M. Adleman, On constructing a molecular computer, Manuscript in circulation, January 1995.

    Google Scholar 

  3. D. Angluin, Finding patterns common to a set of strings, Journal of Computer and System Sciences, 21 (1980), 46–62.

    MathSciNet  MATH  Google Scholar 

  4. A. Atanasiu, V. Mitrana, The modular grammars, Intern. J. Computer Math., 30 (1989), 101–122.

    MATH  Google Scholar 

  5. H. Bordihn, H. Fernau, Accepting grammars with regulation, Intern. J. Computer Math., 53 (1994), 1–18.

    MATH  Google Scholar 

  6. H. Bordihn, H. Fernau, M. Hölzer, Accepting grammar systems, Computers and AI, 1996.

    Google Scholar 

  7. W. Bucher, K. Culik H, H. A. Maurer, D. Wotschke, Concise description of finite languages, Theor. Computer Sci., 14 (1981), 227–246.

    Google Scholar 

  8. L. Cai, The computational complexity of PCGS with regular components, Proc. of Developments in Language Theory Conf., Magdeburg, 1995, 209–219.

    Google Scholar 

  9. L. Cai, The computational complexity of PCGS with linear components, Computers and AI,15, 2–3 (1996), 199–210..

    Google Scholar 

  10. C. Calude, Gh. Nun, Global syntax and semantics for recursively enumerable languages, Fundamenta Informaticae, 42 (1981), 254–254.

    MathSciNet  MATH  Google Scholar 

  11. E. Csuhaj-Varju, Some remarks on cooperating grammar systems, In Proc. Conf. Aut. Lang. Progr. Syst. (I. Peak, F. Gecseg, eds. ), Budapest, 1986, 75–86.

    Google Scholar 

  12. E. Csuhaj-Varju, Cooperating grammar systems. Power and parameters, LNCS 812, Springer-Verlag, Berlin, 1994, 67–84.

    Google Scholar 

  13. E. Csuhaj-Varju, Grammar systems: a multi-agent framework for natural language generation, in [109], 63–78.

    Google Scholar 

  14. E. Csuhaj-Varju, Eco-grammar systems: recent results and perspectives, in [111], 79–103.

    Google Scholar 

  15. E. Csuhaj-Varju, J. Dassow, On cooperating distributed grammar systems, J. Inform. Process. Cybern., EIK, 26 (1990), 49–63.

    MathSciNet  MATH  Google Scholar 

  16. E. Csuhaj-Varju, J. Dassow, J. Kelemen, Gh. Pâun, Stratified grammar systems, Computers and AI, 13 (1994), 409–422.

    MathSciNet  MATH  Google Scholar 

  17. E. Csuhaj-Varju, J. Dassow, J. Kelemen, Gh. Pâun, Grammar Systems. A Grammatical Approach to Distribution and Cooperation, Gordon and Breach, London, 1994.

    MATH  Google Scholar 

  18. E. Csuhaj-Varju, J. Dassow, V. Mitrana, G. Pâun, Cooperation in grammar systems: similarity, universality, timing, Cybernetica, 4 (1993), 271–282.

    MathSciNet  MATH  Google Scholar 

  19. E. Csuhaj-Varju, J. Dassow, Gh. Pâun, Dynamically controlled cooperating distributed grammar systems, Information Sci., 69 (1993), 1–25.

    MathSciNet  MATH  Google Scholar 

  20. E. Csuhaj-Varju, L. Kari, Gh. Pâun, Test tube distributed systems based on splicing, Computers and AI, 15, 23 (1996), 211–232.

    MathSciNet  MATH  Google Scholar 

  21. E. Csuhaj-Varju, J. Kelemen, Cooperating grammar systems: a syntactical framework for the blackboard model of problem solving, In Proc. Conf. Artificial Intelligence and Information-Control Systems of Robots, 89 ( I. Plander, ed.), North-Holland, Amsterdam 1989, 121–127.

    Google Scholar 

  22. E. Csuhaj-Varju, J. Kelemen, On the power of cooperation: a regular representation of r.e. languages, Theor. Computer Sci., 81 (1991), 305–310.

    MathSciNet  MATH  Google Scholar 

  23. E. Csuhaj-Varju, J. Kelemen, A. Kelemenova, Gh. Pâun, Eco-grammar systems: A preview, in Cybernetics and Systems 94 ( R. Trappl, ed.), World Sci. Publ., Singapore, 1994, 941–949.

    Google Scholar 

  24. E. Csuhaj-Varju, J. Kelemen, A. Kelemenova, Gh. Pâun, Eco-grammar systems: A grammatical framework for life-like interactions, Artificial Life, 31 (1996), 1–28.

    Google Scholar 

  25. E. Csuhaj-Varju, J. Kelemen, Gh. Pâun, Grammar systems with WAVE-like communication, Computers and AI, 1996.

    Google Scholar 

  26. E. Csuhaj-Varju, Gh. Pâun, A. Salomaa, Conditional tabled eco-grammar systems, in [111], 227–239.

    Google Scholar 

  27. E. Csuhaj-Varju, Gh. Pâun, A. Salomaa, Conditional tabled eco-grammar systems versus (E)TOL systems, JUCS, 15 (1995), 248–264.

    MATH  Google Scholar 

  28. K. Culik II, T. Harju, Splicing semigroups of dominoes and DNA, Discrete Appl. Math., 31 (1991), 261–277.

    MathSciNet  MATH  Google Scholar 

  29. J. Dassow, Cooperating distributed grammar systems with hypothesis languages, J. Exper. Th. AI, 3 (1991), 11–16.

    Google Scholar 

  30. J. Dassow, A remark on cooperating distributed grammar systems controlled by graphs, Wiss. Z. der TU Magdeburg, 35 (1991), 4–6.

    MathSciNet  MATH  Google Scholar 

  31. J. Dassow, An example of an eco-grammar system: a can collecting robot, in [111], 240–244.

    Google Scholar 

  32. J. Dassow, J. Kelemen, Cooperating distributed grammar systems: a link between formal languages and artificial intelligence, Bulletin of EATCS, 45 (1991), 131–145.

    MATH  Google Scholar 

  33. J. Dassow, J. Kelemen, Gh. Pâun, On parallelism in colonies, Cybernetics and Systems, 24 (1993), 37–49.

    MathSciNet  MATH  Google Scholar 

  34. J. Dassow, V. Mihalache, Eco-grammar systems, matrix grammars and EOL systems, in [111], 210–226.

    Google Scholar 

  35. J. Dassow, V. Mitrana, Splicing grammar systems, Computers and AI, 15, 23 (1996), 109–122.

    MathSciNet  MATH  Google Scholar 

  36. J. Dassow, V. Mitrana, Cooperating distributed pushdown automata systems, submitted, 1995.

    Google Scholar 

  37. J. Dassow, V. Mitrana, Deterministic pushdown automata systems, submitted, 1995.

    Google Scholar 

  38. J. Dassow, V. Mitrana, “Call by name” and “call by value” in cooperating distributed grammar systems, Ann. Univ. Buc., Matern.-Inform. Series, 45, 1 (1996), 29–40.

    Google Scholar 

  39. J. Dassow, V. Mitrana, Fairness in grammar systems, submitted, 1995.

    Google Scholar 

  40. J. Dassow, V. Mitrana, Gh. Pâun, Szilard languages associated to cooperating distributed grammar systems, Stud. Cercet. Mat., 45, 5 (1993), 403–413.

    MathSciNet  MATH  Google Scholar 

  41. J. Dassow, Gh. Pâun, Regulated Rewriting in Formal Language Theory, Springer-Verlag, Berlin, Heidelberg, 1989.

    MATH  Google Scholar 

  42. J. Dassow, Gh. Nun, Cooperating distributed grammar systems with registers, Found. Control Engineering, 15 (1990), 19–38.

    MathSciNet  MATH  Google Scholar 

  43. J. Dassow, Gh. Pâun, On the succinctness of descriptions of context-free languages by cooperating distributed grammar systems, Computers and AI, 10 (1991), 513–527.

    MathSciNet  MATH  Google Scholar 

  44. J. Dassow, Gh. Pâun, On some variants of cooperating distributed grammar systems, Stud. Cercet. Mat., 42, 2 (1990), 153–165.

    MathSciNet  MATH  Google Scholar 

  45. J. Dassow, Gh. Pâun, St. Skalla, On the size of components of cooperating grammar systems, LNCS 812, Springer-Verlag, Berlin, 1994, 325–343.

    Google Scholar 

  46. S. Dumitrescu, CD and PC grammar systems, PHD Thesis, Univ. of Bucharest, Faculty of Mathematics, 1996.

    MATH  Google Scholar 

  47. S. Dumitrescu, Non-returning parallel communicating grammar systems can be simulated by returning systems, Theor. Computer Sci.,to appear.

    Google Scholar 

  48. S. Dumitrescu, Gh. Pâun, On the power of parallel communicating grammar systems with right-linear components, submitted, 1995.

    Google Scholar 

  49. S. Dumitrescu, Gh. Nun, A. Salomaa, Pattern languages versus parallel communicating grammar systems, Intern. J. Found, Computer Sci.,to appear.

    Google Scholar 

  50. L. Errico, WAVE: An Overview of the Model and the Language, CSRG, Dept. Electronic and Electr. Eng., Univ. of Surrey, UK, 1993.

    Google Scholar 

  51. L. Errico, C. Jesshope, Towards a new architecture for symbolic processing, In Proc. Con f. Artificial Intelligence and Information-Control Systems of Robots ‘84 ( I. Plander, ed.), World Sci. Publ., Singapore, 1994, 31–40.

    Google Scholar 

  52. J. D. Farmer, A. d’A Belin, Artificial Life: the coming evolution,in Proc. in Cellebration of Muray Gell-Man’s 60th Birthday,Cambridge Univ. Press., Cambridge, 1990.

    Google Scholar 

  53. H. Fernau, M. Holzer, H. Bordihn, Accepting multi-agent systems: the case of CD grammar systems, Computers and AI, 15, 23 (1996), 123–140.

    MATH  Google Scholar 

  54. R. Freund, Multi-level eco-array grammars, in [111], 175–201.

    Google Scholar 

  55. R. Freund, L. Kari, Gh. Pâun, DNA computing based on splicing: the existence of universal computers, submitted, 1995.

    Google Scholar 

  56. R. Freund, Gh. [’Ann, A variant of team cooperation in grammar systems, JUGS, 1, 3 (1995), 105–130.

    MathSciNet  MATH  Google Scholar 

  57. R. Freund, Gh. PAun, C. M. Procopiuc, O. Procopiuc, Parallel communicating grammar systems with context-sensitive components, in [111], 166–174.

    Google Scholar 

  58. G. Georgescu, The generative power of small grammar systems, in [111], 152165.

    Google Scholar 

  59. G. Georgescu, A sufficient condition for the regularity of PCGS languages, J. Automata, Languages, Combinatorics,to appear.

    Google Scholar 

  60. J. Gruska, Descriptional complexity of context-free languages, Proc. MFCS 73, High Tatras, 1973, 71–84.

    Google Scholar 

  61. D. Hauschild, M. Jantzen, Petri nets algorithms in the theory of matrix grammars, Acta Informatica, 31 (1994), 719–728.

    MathSciNet  Google Scholar 

  62. W. D. Hillis, The Connection Machine. The MIT Press, Cambridge, Mass., 1985.

    Google Scholar 

  63. T. Head, Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors, Bull. Math. Biology, 49 (1987), 737–759.

    MathSciNet  MATH  Google Scholar 

  64. J. Hromkovic, Descriptional and computational complexity measures for distributive generation of languages, in Proc. of Developments in Language Theory Conf., Magdeburg, 1995.

    Google Scholar 

  65. J. Hromkovic, J. Kari, L. Kari, Some hierarchies for the communicating complexity measures of cooperating grammar systems, Theor. Computer Sci., 127 (1994), 123–147.

    MATH  Google Scholar 

  66. J. Hromkovic, J. Kari, L. Kari, D. Pardubska, Two lower bounds on distributive generation of languages, Proc. MFCS 94, LNCS 841, Springer-Verlag, Berlin, 1994, 423–432.

    Google Scholar 

  67. J. Hromkovic, D. Wierzchula, On nondeterministic linear time, real time and parallel communicating grammar systems, in [109], 184–190.

    Google Scholar 

  68. L. Ilie, Collapsing hierarchies in parallel communicating grammar systems with communication by command, Computers and AI,15, 23 (1996), 173184.

    Google Scholar 

  69. L. Ilie, A. Salomaa, 2-testability and relabeling produce everything, submitted, 1995.

    Google Scholar 

  70. C. M. Ionescu, O. Procopiuc, Bounded communication in parallel communicating grammar systems, J. Inform. Process. Cybern., EIK, 30 (1994), 97–110.

    MATH  Google Scholar 

  71. L. Kari, A. Mateescu, Gh. PAun, A. Salomaa, Teams in cooperating grammar systems, J. Exper. Th. AI, 7 (1995), 347–359.

    MATH  Google Scholar 

  72. J. Kari, L. Sântean, The impact of the number of cooperating grammars on the generative power, Theor. Computer Sci., 98 (1992), 621–633.

    MathSciNet  MATH  Google Scholar 

  73. J. Kelemen, A. Kelemenova, A subsumption architecture for generative symbol systems, in Cybernetics and Systems Research 92 ( R. Trappl, ed.), World Sci. Publ., Singapore, 1992, 1529–1536.

    Google Scholar 

  74. J. Kelemen, R. Miichova, Bibliography of grammar systems, Bulletin of EATCS, 49 (1992), 210–218.

    MATH  Google Scholar 

  75. A. Kelemenova, E. Csuhaj-Varju, Languages of colonies, Theo r. Computer Sci., 134 (1994), 119–130.

    MathSciNet  MATH  Google Scholar 

  76. A. Kelemenova, J. Kelemen, From colonies to eco-grammar systems. An overview, LNCS 812, Springer-Verlag, Berlin, 1994, 213–231.

    Google Scholar 

  77. C. Langton, Artificial life, in Artificial Life ( C. Langton, ed.), Santa Fe Institute Studies in the Sciences of Complexity, Addison Wesley Publ., 1989.

    MATH  Google Scholar 

  78. R. J. Lipton, Speeding up computations via molecular biology, Manuscript in circulation, December 1994.

    Google Scholar 

  79. M. Malita, Gh. Stefan, The eco-chip: a physical support for artificial life systems, in [111], 260–275.

    Google Scholar 

  80. A. Mateescu, A survey of teams in cooperating distributed grammar systems, in [111], 137–151.

    Google Scholar 

  81. A. Mateescu, Teams in cooperating distributed grammar systems; an overview, Proc. Decentralized Intelligent and Multi-Agent Systems, DIMAS ‘85, Cracow, 1995, 309–323.

    Google Scholar 

  82. R. Meersman, G. Rozenberg, Cooperating grammar systems, Proc. MFCS ‘78, LNCS 64, Springer-Verlag, Berlin, 1978, 364–374.

    Google Scholar 

  83. R. Meersman, G. Rozenberg, D. Vermeir, Cooperating grammar systems, Techn. Report, 78–12, Univ. Antwerp, Dept. of Math., 1978.

    Google Scholar 

  84. M. Middendorf, Supersequences, runs and CD grammar systems, in Developments in Theoretical Computer Science ( J. Dassow, A. Kelemenova, eds.), Gordon and Breach, London, 1994, 101–113.

    Google Scholar 

  85. V. Mihalache, Matrix grammars versus parallel communicating grammar systems, in [109], 293–318.

    Google Scholar 

  86. V. Mihalache, Extended conditional tabled eco-grammar systems, J. Inform. Processing Cybern., 30, 4 (1994), 213–229.

    MATH  Google Scholar 

  87. V Mihalache, General Artificial Intelligence systems as eco-grammar systems, in [111], 245–259.

    Google Scholar 

  88. V. Mihalache, On parallel communicating grammar systems with context-free components, in [113], 258–270.

    Google Scholar 

  89. V. Mihalache, Szilard languages associated to parallel communicating grammar systems, Proc. of Developments in Language Theory Conf., Magdeburg, 1995, 247–256.

    Google Scholar 

  90. V. Mihalache, On the generative capacity of parallel communicating grammar systems with regular components, Computers and AI, 15, 23 (1996), 155–172.

    MATH  Google Scholar 

  91. V. Mihalache, Terminal versus nonterminal symbols in parallel communicating grammar systems, Rev. Rouen. Math. Pures Appl., 1996.

    Google Scholar 

  92. V. Mihalache, Variants of parallel communicating grammar systems, Mathematical Linguistics Conf., Tarragona, 1996.

    Google Scholar 

  93. V. Mihalache, Parallel communicating grammar systems with query words, Ann. Univ. Buc., Matem.-Inform. Series, 45, 1 (1996), 81–92.

    MathSciNet  Google Scholar 

  94. Grammargsm Pairs, Ann. Univ. Buc., Ser. Matem.-Inform., 39, 40 (1992), 64–71.

    Google Scholar 

  95. V. Mitrana, Hybrid cooperating distributed grammar systems, Computers and AI, 2 (1993), 83–88.

    MathSciNet  MATH  Google Scholar 

  96. V. Mitrana, Eco-pattern systems, in [111], 202–209.

    Google Scholar 

  97. V. Mitrana, Similarity in grammar systems, Fundamenta Informaticae, 24 (1995), 251–257.

    MathSciNet  MATH  Google Scholar 

  98. V. Mitrana, Gh. Pâun, G. Rozenberg, Structuring grammar systems by priorities and hierarchies, Acta Cybernetica, 11 (1994), 189–204.

    MathSciNet  MATH  Google Scholar 

  99. P. H. Nii, Blackboard systems, In The Handbook of AI, vol. 4 ( A. Barr, P. R. Cohen, E. A. Feigenbaum, eds.), Addison-Wesley, Reading, Mass., 1989.

    Google Scholar 

  100. D. Pardubska, On the power of communication structure for distributive generation of languages, In Developments in Language Theory ( G. Rozenberg, A. Salomaa, eds.), World Sci. Publ., Singapore, 1994, 90–101.

    Google Scholar 

  101. D. Pardubska, Communication complexity hierarchies for distributive generation of languages, Fundamenta Informaticae,to appear.

    Google Scholar 

  102. Gh. Pâun, A new type of generative device: valence grammars, Rev. Rouen. Math. Pures Appl., 25, 6 (1980), 911–924.

    MATH  Google Scholar 

  103. Gh. Pâun, Parallel communicating grammar systems: the context-free case, Found. Control Engineering, 14, 1 (1989), 39–50.

    MathSciNet  MATH  Google Scholar 

  104. Gh. Nun, On the power of synchronization in parallel communicating grammar systems, Stud. Cerc. Matem., 41, 3 (1989), 191–197.

    MathSciNet  Google Scholar 

  105. Gh. Nun, Non-centralized parallel communicating grammar systems, Bulletin of EATCS, 40 (1990), 257–264.

    MATH  Google Scholar 

  106. Gh. Pâun, On the syntactic complexity of parallel communicating grammar systems, Kybernetika, 28 (1992), 155–166.

    MathSciNet  MATH  Google Scholar 

  107. Gh. Nun, Parallel communicating systems of L systems, in Lindenmayer systems. Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology ( G. Rozenberg, A. Salomaa, eds.), Springer-Verlag, Berlin, 1992, 405–418.

    Google Scholar 

  108. Gh. Nun, On the synchronization in parallel communicating grammar systems, Acta Informatica, 30 (1993), 351–367.

    MathSciNet  Google Scholar 

  109. Gh. Nun (ed.), Mathematical Aspects of Natural and Formal Languages, World Sci. Publ., Singapore, 1994.

    Google Scholar 

  110. Gh. Nun, On the generative capacity of colonies, Kybernetika, 31 (1995), 83–97.

    MathSciNet  Google Scholar 

  111. Gh. Nun (ed.), Artificial Life. Grammatical Models, The Black Sea Univ. Press, Bucharest, 1995.

    Google Scholar 

  112. Gh. Nun, On the generative capacity of hybrid CD grammar systems, J. Inform. Process. Cybern., EIK, 30, 4 (1994), 231–244.

    Google Scholar 

  113. Gh. Pâun (ed.), Mathematical Linguistics and Related Topics, The Publ. House of the Romanian Academy, Bucharest, 1995.

    Google Scholar 

  114. Gh. Nun, Grammar systems: A grammatical approach to distribution and cooperation, Proc. ICALP ‘85 Conf., LNCS, 944 (1995), 429–443.

    MathSciNet  Google Scholar 

  115. Gh. Pâun, Generating languages in a distributed way: grammar systems, XIth Congress on Natural and Formal Languages, Tortosa, 1995, 45–67.

    Google Scholar 

  116. Gh. Nun, Parallel comunicating grammar systems. A survey, XIth Congress on Natural and Formal Languages, Tortosa, 1995, 257–283.

    Google Scholar 

  117. Gh. Pâun, On the splicing operation, Discrete Appl. Math., 70 (1996), 57–79.

    MathSciNet  MATH  Google Scholar 

  118. Gh. Nun, Regular extended H systems are computationally universal, J. Automata, Languages, Combinatorics, 11 (1996), 27–36.

    MathSciNet  Google Scholar 

  119. Gh. Nun On the power of the splicing operation, Intern. J. Computer Math., 59 (1995), 27–35.

    Google Scholar 

  120. Gh. Pâun, L. Polkowski, A. Skowron, Parallel communicating grammar systems with negotiation, Fundamenta Informaticae, 1996.

    Google Scholar 

  121. Gh. Nun, G. Rozenberg, Prescribed teams of grammars, Acta Informatica, 31 (1994), 525–537.

    MathSciNet  MATH  Google Scholar 

  122. Gh. Nun, G. Rozenberg, A. Salomaa, Computing by splicing, Intern. J. Computer Sci., 1996, 168, 2 (1996), 321–336.

    MathSciNet  MATH  Google Scholar 

  123. Gh. Nun, A. Salomaa, S. Vicolov, On the generative capacity of parallel communicating grammar systems, Intern. J. Computer Math., 45 (1992), 4959.

    Google Scholar 

  124. Gh. Nun, L. Sântean, Parallel communicating grammar systems: the regular case, Ann. Univ. Bue. Ser. Matem.-Inform., 38 (1989), 55–63.

    MathSciNet  MATH  Google Scholar 

  125. Gh. Nun, L. Sântean, Further remarks about parallel communicating grammar systems, Intern. J. Computer Math., 34 (1990), 187–203.

    MATH  Google Scholar 

  126. D. Pixton, Regularity of splicing languages, Discrete Appl. Math., 1995, 69 (1996), 101–124.

    MathSciNet  MATH  Google Scholar 

  127. O. Procopiuc, C. M. Ionescu, F. L. Tiplea, Parallel communicating grammar systems: the context-sensitive case, Intern. J. Computer Math, 49 (1993), 145–156.

    MATH  Google Scholar 

  128. G. Rozenberg, K. Ruohonen, A. Salomaa, Developmental systems with fragmentation, Intern. J. Computer Math., 5 (1976), 177–191.

    MathSciNet  MATH  Google Scholar 

  129. G. Rozenberg, A. Salomaa, The Mathematical Theory of L Systems, Academic Press, New York, 1980.

    MATH  Google Scholar 

  130. A. Salomaa, Formal Languages, Academic Press, New York, 1973.

    MATH  Google Scholar 

  131. L. Sântean, Parallel communicating systems, Bulletin of EATCS, 42 (1990), 160–171.

    MATH  Google Scholar 

  132. P. S. Sapaty, The WAVE Paradigm, Internal Report 17/92, Dept. Informatics, University of Karlsruhe, 1992.

    Google Scholar 

  133. S. Skalla, On the number of active nonterminals of cooperating distributed grammar systems, in Artificial Intelligence and Information-Control Systems of Robots 94 ( I. Plander, ed.), World Sci. Publ., Singapore, 1994, 367–374.

    Google Scholar 

  134. A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc., Ser. 2, 42 (1936), 230–265.

    MathSciNet  MATH  Google Scholar 

  135. F. L. Tiplea, C. Ene, A coverability structure for parallel communicating grammar systems, J. Inform. Process. Cybern., EIK, 29 (1993), 303–315.

    MATH  Google Scholar 

  136. F. L. Tiplea, C. Ene, C. M. Ionescu, O. Procopiuc, Some decision problems for parallel communicating grammar systems, Theor. Computer Sci., 134 (1994), 365–385.

    MathSciNet  MATH  Google Scholar 

  137. F. L. Tiplea, O. Procopiuc, C. M. Procopiuc, C. Ene, On the power and complexity of parallel communicating grammar systems, in [111], 53–78.

    Google Scholar 

  138. G. Vaszil, Parallel communicating grammar systems without a master, Computers and AI, 15, 23 (1996), 185–198.

    MathSciNet  MATH  Google Scholar 

  139. G. Vaszil, The simulation of a non-returning parallel communicating grammar system with a returning system in case of linear component grammars, submitted, 1995.

    Google Scholar 

  140. S. Vicolov, Non-centralized parallel grammar systems, Stud. Cercet. Matera., 44 (1992), 455–462.

    MathSciNet  MATH  Google Scholar 

  141. D. Wâtjen, On cooperating distributed limited OL systems, J. Inform. Process. Cybern. EIK, 29 (1993), 129–142.

    MATH  Google Scholar 

  142. Connection Machine Model CM-2 Technical Summary, Thinking Machines Corporation, Cambridge, Mass., 1987.

    Google Scholar 

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Dassow, J., Păun, G., Rozenberg, G. (1997). Grammar Systems. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07675-0_4

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