Skip to main content
SpringerLink
Log in

Families Generated by Grammars and L Systems

  • Chapter
  • First Online:
Handbook of Formal Languages

Abstract

Grammars appear in many chapters of this Handbook, often constituting the key notion of the chapter. Usually a specific language, L(G), is associated to a grammar G. The language L(G) is generated by the grammar G,obtained from a specific starting point by rules specified in the grammar. In this chapter we take a more general point of view. A grammar G defines a collection of structurally similar grammars G’, called interpretations of G. Each of the interpretations G’,in turn, generates a language L(G’) in the usual way. In this chapter we consider the family \( \mathcal{L} \) (G) of languages L(G’) generated by the interpretations G’ of G. The family \( \mathcal{L} \) (G) is referred to as the grammatical family associated to G. Thus, from the point of view taken in this chapter, grammars generate families of languages rather than single languages. When grammars are considered in this way, the term “grammar form” rather than “grammar” will be used. As constructs grammar forms and grammars are identical. However, they are applied in different ways. We will consider also L forms, that is L systems applied similarly, defining language families via interpretations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. V. Aho, J. D. Ullman, The Theory of Parsing,Translation, and Computing, Vol. I: Parsing, Prentice-Hall, Inc., Englewood Cliffs, N. J. 1972.

    Google Scholar 

  2. J. Albert, H. Maurer, The class of CF languages is not an EOL family, Inform. Processing Letters., 6 1978, 190–195.

    Article  Google Scholar 

  3. A. B. Cremers, S. Ginsburg, Characterizations of context-free grammatical families, IEEE 15th Annual Symp. Switching and Automata Th., New Orleans 1974.

    Google Scholar 

  4. A. B. Cremers, S. Ginsburg, Context-free grammar forms, J. Computer System Sci.,11 1975, 86–116.

    Article  MathSciNet  Google Scholar 

  5. K. Culik II H. A. Maurer, T. Ottmann, K. Ruohonen, A. Salomaa, Isomorphism, form equivalence and sequence equivalence of PDOL forms, Theor. Computer Sci., 6 1978, 143–174.

    Article  Google Scholar 

  6. J. Dassow, Gh. Páun, Regulated Rewriting in Formal Language Theory, Springer-Verlag, Berlin 1989.

    Book  Google Scholar 

  7. J. Dassow, Gh. Páun, A. Salomaa, Grammars with Controlled Derivations, in this Handbook.

    Google Scholar 

  8. A. Gabrielian, S. Ginsburg, Grammar schemata, Journal of the ACM, 21 1974, 213–226.

    Article  MathSciNet  Google Scholar 

  9. S. Ginsburg, B. L. Leon, O. Mayer, D. Wotschke, On strict interpretations of grammar forms, Math. Systems Th., 12 1979, 233–252.

    Article  MathSciNet  Google Scholar 

  10. J. N. Gray, M. A. Harrison, On the covering and reduction problems for context-free grammars, Journal of the ACM, 19, 4 1972, 675–698.

    Article  MathSciNet  Google Scholar 

  11. S. A. Greibach, Control sets on context-free grammar forms, J. Computer System Sci., 15 1977, 35–98.

    Article  MathSciNet  Google Scholar 

  12. G. Hotz, Eindeutigkeit and Mehrdeutigkeit Formaler Sprachen, EIK, 2 1966, 235–247.

    MathSciNet  MATH  Google Scholar 

  13. R. Leipälä, On context-free matrix forms, Inform. Control, 39 1978, 158–176.

    Article  MathSciNet  Google Scholar 

  14. R. Leipälä, On the generative capacity of context-free matrix forms, Intern. J. Computer Math., 7 1979, 251–269.

    Article  MathSciNet  Google Scholar 

  15. R. Leipälä, Generation of context-free languages by matrix forms, Ann. Univ. Turku, Ser. AI, 179 1979.

    MATH  Google Scholar 

  16. R. Leipälä, Studies on Context-free Matrix Forms, PhD Thesis, University of Turku 1979.

    MATH  Google Scholar 

  17. H. A. Maurer, Th. Ottmann, A. Salomaa, On the form equivalence of L forms, Theor. Computer Sci., 4 1977, 199–225.

    Article  MathSciNet  Google Scholar 

  18. H. A. Maurer, M. Penttonen, A. Salomaa, D. Wood, On non context-free grammar forms, Math. Syst. Th., 12 1979, 297–324.

    Article  MathSciNet  Google Scholar 

  19. H. A. Maurer, A. Salomaa, D. Wood, EOL forms, Acta Informatica, 8 1977, 75–96.

    MATH  Google Scholar 

  20. H. A. Maurer, A. Salomaa, D. Wood, Uniform interpretations of L forms, Inform. Control, 36 1978, 157–173.

    Article  MathSciNet  Google Scholar 

  21. H. A. Maurer, A. Salomaa, D. Wood, ETOL forms, J. Computer System Sci., 16 1978, 345–361.

    Article  MathSciNet  Google Scholar 

  22. H. A. Maurer, A. Salomaa, D. Wood, Good EOL forms, SIAM J. Comput., 7 1978, 158–166.

    Article  MathSciNet  Google Scholar 

  23. H. A. Maurer, A. Salomaa, D. Wood, Relative goodness of EOL forms, RA IRO, 12 1978, 291–304.

    MathSciNet  MATH  Google Scholar 

  24. H. A. Maurer, A. Salomaa, D. Wood, Context-dependent L forms, Inform. Control, 42 1979, 97–118.

    Article  MathSciNet  Google Scholar 

  25. H. A. Maurer, A. Salomaa, D. Wood, On generators and generative capacity of EOL forms, Acta Informatica, 13 1980, 87–107.

    Article  MathSciNet  Google Scholar 

  26. H. A. Maurer, A. Salomaa, D. Wood, Context-free grammar forms with strict interpretations, J. Computer System Sci.,21 1980, 110–135.

    Article  MathSciNet  Google Scholar 

  27. H. A. Maurer, A. Salomaa, D. Wood, Synchronized EOL forms, Theor. Com puter Sci., 12 1980, 135–159.

    Article  MathSciNet  Google Scholar 

  28. H. A. Maurer, A. Salomaa, D. Wood, Decidability and density in two-symbol grammar forms, Discrete Applied Math.,3 1981, 289–299.

    Article  MathSciNet  Google Scholar 

  29. H. A. Maurer, A. Salomaa, D. Wood, MSW spaces, Inform. Control, 46 1981, 200–218.

    MathSciNet  MATH  Google Scholar 

  30. H. A. Maurer, A. Salomaa, D. Wood, Uniform interpretations of grammar forms, SIAM J. Comput., 10 1981, 483–502.

    Article  MathSciNet  Google Scholar 

  31. H. A. Maurer, A. Salomaa, D. Wood, Synchronized EOL forms under uniform interpretation, RAIRO, Th. Informatics, 15 1981, 337–353.

    Google Scholar 

  32. H. A. Maurer, A. Salomaa, D. Wood, Derivation languages of grammar forms, Intern. J. Computer Math., 9 1981, 117–130.

    Article  MathSciNet  Google Scholar 

  33. H. A. Maurer, A. Salomaa, D. Wood, Colorings and interpretations - a connection between graphs and grammar forms, Discrete Applied Math., 3 1981, 119–135.

    Article  MathSciNet  Google Scholar 

  34. H. A. Maurer, A. Salomaa, D. Wood, On predecessors of finite grammar forms, Inform. Control, 50 1981, 259–275.

    Article  MathSciNet  Google Scholar 

  35. H. A. Maurer, A. Salomaa, D. Wood, Completeness of context-free grammar forms, J. Computer System Sci., 23 1981, 1–10.

    Article  MathSciNet  Google Scholar 

  36. H. A. Maurer, A. Salomaa, D. Wood, Dense hierarchies of grammatical families, Journal of the ACM, 29 1982, 118–126.

    Article  MathSciNet  Google Scholar 

  37. H. A. Maurer, A. Salomaa, D. Wood, Finitary and infinitary interpretations of languages, Math. Systems Th., 15 1982, 251–265.

    Article  MathSciNet  Google Scholar 

  38. H. A. Maurer, A. Salomaa, D. Wood, A supernormal form theorem for context-free grammars, Journal of the ACM, 30 1983, 95–102.

    Article  MathSciNet  Google Scholar 

  39. H. A. Maurer, A. Salomaa, D. Wood, On finite grammar forms, Intern. J. Computer Math., 12 1983, 227–240.

    MATH  Google Scholar 

  40. V. Niemi, The undecidability of form equivalence for context-free and EOL forms, Theor. Computer Sci., 32 1984, 261–277.

    Article  MathSciNet  Google Scholar 

  41. V. Niemi, Density of grammar forms, I and II, Intern. J. Computer Math., 20 1986,3–21 and 91–114.

    Article  Google Scholar 

  42. V. Niemi, Maximal dense intervals of grammar forms, Lecture Notes in Computer Science, Springer-Verlag, Berlin 317 1988, 424–438.

    Article  MathSciNet  Google Scholar 

  43. Th. Ottmann, A. Salomaa, D. Wood, Sub-regular grammar forms, Inform. Processing Letters, 12 1981, 184–187.

    Article  Google Scholar 

  44. M. Penttonen, On derivation languages corresponding to context-free grammars, Acta Inforrnatica, 3 1974, 285–291.

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  46. A.Salomaa, On color-families of graphs, Ann. Acad. Scient. Fennicae A16 1981, 135–148.

    MathSciNet  MATH  Google Scholar 

  47. E. Shamir, On sequential languages, Z. Phonetik Sprachwiss. Kommunikat., 18 1965,61–69.

    MathSciNet  Google Scholar 

  48. H. Walter, Topologies of formal languages, Math. Systems Th., 9 1975, 142–158.

    Article  MathSciNet  Google Scholar 

  49. E. Welzl, Color-families are dense, Theor. Computer Sci., 17 1982, 29–41.

    Article  MathSciNet  Google Scholar 

  50. D. Wood, Grammar and L Forms: An Introduction, Lecture Notes in Computer Science, Springer-Verlag, Berlin 91 1980.

    Chapter  Google Scholar 

Download references

Authors
  1. Gheorghe Păun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arto Salomaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, Leiden, RA, NL-2300, The Netherlands

    Grzegorz Rozenberg

  2. Turku Centre for Computer Science Data City, Turku, FIN-20520, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Păun, G., Salomaa, A. (1997). Families Generated by Grammars and L Systems. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59136-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59136-5_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63863-3

  • Online ISBN: 978-3-642-59136-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation