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Controlled fuzzy parallel rewriting

  • 1. Regulated Rewriting
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New Trends in Formal Languages

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1218))

Abstract

We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show that (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages.

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References

  1. Asveld, P.R.J.: Controlled iteration grammars and full hyper-AFL's, Inform. Contr. 34 (1977) 248–269.

    Google Scholar 

  2. Asveld, P.R.J.: An algebraic approach to incomparable families of formal languages, pp. 455–475 in [22].

    Google Scholar 

  3. Asveld, P.R.J.: Towards robustness in parsing — Fuzzifying context-free language recognition, pp. 443–453 in: J. Dassow, G. Rozenberg & A. Salomaa (eds.): Developments in Language Theory II — At the Crossroads of Mathematics, Computer Science and Biology (1996), World Scientific, Singapore.

    Google Scholar 

  4. Asveld, P.R.J.: A fuzzy approach to erroneous inputs in context-free language recognition, pp. 14–25 in: Proc. 4th Internat. Workshop on Parsing Technologies (1995), Prague/Karlovy Vary, Czech Republic.

    Google Scholar 

  5. Asveld, P.R.J.: The non-self-embedding property for generalized fuzzy context-free grammars, Memorandum Informatica 96-08 (1996), Dept. of Comp. Sci., Twente University of Technology, Enschede, the Netherlands. Presented at 8th Internat. Conf. on Automata and Formal Languages (1996), Salgótarján, Hungary.

    Google Scholar 

  6. Asveld, P.R.J.: A note on Full Abstract Families of Fuzzy Languages (Full AFFL). In preparation.

    Google Scholar 

  7. Dassow, J. & Păun, G.: Regulated Rewriting in Formal Language Theory (1989), Springer-Verlag, Berlin, etc.

    Google Scholar 

  8. Gerla, G.: Fuzzy grammars and recursively enumerable fuzzy languages, Inform. Sci. 60 (1992) 137–143.

    Google Scholar 

  9. Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages (1975), North-Holland, Amsterdam.

    Google Scholar 

  10. Ginsburg, S. & Rozenberg, G.: TOL schemes and control sets, Inform. Contr. 27 (1975) 109–125.

    Google Scholar 

  11. Goguen, J.A.: L-fuzzy sets, J. Math. Analysis Appl. 18 (1967) 145–174.

    Google Scholar 

  12. Harrison, M.A.: Introduction to Formal Language Theory (1978), Addison-Wesley, Reading, Mass.

    Google Scholar 

  13. Herman, G.T. & Rozenberg, G.: Developmental Systems and Languages (1975), North-Holland, Amsterdam.

    Google Scholar 

  14. Hopcroft, J.E. & Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation (1979), Addison-Wesley, Reading, Mass.

    Google Scholar 

  15. Lindenmayer, A.: Mathematical models for cellular interactions in development, Parts I and II, J. Theor. Biology 18 (1968) 280–315.

    Google Scholar 

  16. Lindenmayer, A.: Developmental systems without cellular interaction, their languages and grammars, J. Theor. Biology 30 (1971) 455–484.

    Google Scholar 

  17. Lee, E.T. & Zadeh, L.A.: Note on fuzzy languages, Inform. Sci. 1 (1969) 421–434.

    Google Scholar 

  18. Nielsen, M.: EOL systems with control devices, Acta Inform. 4 (1975) 373–386.

    Google Scholar 

  19. Prasad, N., Mahajan, M. & Krithivasan, K.: Fuzzy L-systems, Internat. J. Comput. Math. 36 (1990) 139–161.

    Google Scholar 

  20. Rozenberg, G.: Extensions of tabled OL-systems and languages, Internat. J. Comp. Inform. Sci. 2 (1973) 311–336.

    Google Scholar 

  21. Rozenberg, G. & Salomaa, A.: The Mathematical Theory of L Systems (1980), Academic Press, New York.

    Google Scholar 

  22. Rozenberg, G. & Salomaa, A. (eds.): Lindenmayer Systems — Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology (1992), Springer-Verlag, Berlin, etc.

    Google Scholar 

  23. Salomaa, A.: Formal Languages (1973), Academic Press, New York.

    Google Scholar 

  24. Wood, D.: A note on Lindenmayer systems, Szilard languages, spectra, and equivalence, Internat. J. Comp. Inform. Sci. 4 (1975) 53–62.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Twente University of Technology, P.O. Box 217, 7500, AE Enschede, The Netherlands

    Peter R. J. Asveld

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  1. Peter R. J. Asveld
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Gheorghe Păun Arto Salomaa

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© 1997 Springer-Verlag Berlin Heidelberg

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Asveld, P.R.J. (1997). Controlled fuzzy parallel rewriting. In: Păun, G., Salomaa, A. (eds) New Trends in Formal Languages. Lecture Notes in Computer Science, vol 1218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62844-4_5

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  • DOI: https://doi.org/10.1007/3-540-62844-4_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62844-6

  • Online ISBN: 978-3-540-68703-0

  • eBook Packages: Springer Book Archive

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