Skip to main content
Log in

Complexity of some problems concerningL systems

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

We determine the computational complexity of membership, emptiness and infiniteness for several types ofL systems. TheL systems we consider are ED0L, E0L, EDT0L, and ET0L, with and without empty productions. For each problem and each type of system we establish both upper and lower bounds on the time or memory required for solution by Turing machines.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  2. H. Alt and K. Mehlhorn, Lower bounds for the space complexity of context-free recognition, in S. Michaelson, and R. Milner,Automata, Languages and Programming, (3rd Coll., Edinburgh), University Press, Edinburgh, Scotland, 338–354, 1976.

  3. T. Harju, A polynomial recognition algorithm for the EDT0L languages, Elektro. Inform. Kybernetik 13, 169–177, 1977.

    Google Scholar 

  4. G. T. Herman and G. Rozenberg,Developmental Systems and Languages, North-Holland, Amsterdan, 1975.

    Google Scholar 

  5. J. E. Hopcroft and J. D. Ullman,Formal Languages and their Relation to Automata, Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

  6. N. D. Jones and W. T Laaser, Complete problems for deterministic polynomial Time,Theoretical Comp. Sci. 3, 105–118, 1976.

    Google Scholar 

  7. N. D. Jones and S. Skyum, Recognition of deterministic ET0L languages in logarithmic space.Information and Control 35, 177–181, 1977.

    Google Scholar 

  8. N. D. Jones and S. Skyum, Complexity of some problems concerningL systems, A. Salomaa and M. Steinby,Automata, Languages and Programming, (4th Coll., Turku), Springer Lecture Notes in Computer Science 52, 301–308, 1977.

    Google Scholar 

  9. P. M. Lewis III R. E. Stearns and J. Hartmanis, Memory bounds for the recognition of context-free and context-sensitive languages,IEEE Conference Record on Switching Circuit Theory and Logical Design, Ann Arbor, Michigan, 191–202, 1965.

  10. A. R. Meyer and L. J. Stockmeyer, The Equivalence problem for regular expressions with squaring requires exponential space,Conf. Rec. 13th Annual IEEE Symposium on Switching and Automata Theory, Baltimore, 125–129, 1972.

  11. J. Seiferas, M. Fischer, and A. Meyer, Refinements of nondeterministic time and space hierarchies,Conf. Rec. 14th Annual IEEE Symposium on Switching and Automata Theory, Iowa, 130–137, 1973.

  12. L. J. Stockmeyer and A. R. Meyer, Word problems requiring exponential time,Proc. 5th Annual ACM Symposium on Theory of Computing, Austin, May 1–9, 1973.

  13. I. H. Sudborough, A note on tape-bounded complexity classes and linear context-free languages,J. ACM 22, 499–500, 1975.

    Google Scholar 

  14. I. H. Sudborough, The time and tape complexity of developmental languages, in: Salomaa, A., Steinby, M.,Automata, Languages and Programming, (4th Coll., Turku), Springer Lecture Notes in Computer Science 52, 509–523, 1977.

    Google Scholar 

  15. L. G. Valiant, General context-free recognition in less than cubic time.J. Computer and Systems Sciences 10, 308–315, 1975.

    Google Scholar 

  16. J. van Leeuwen, Deterministically recognizing E0L languages in timeO(n 3.81). Tech. Rep. Math. Centrum, Amsterdam (1975).

  17. J. van Leeuwen, The membership question for ET0L languages is polynomially complete,Information Processing Letters 3, 138–143, 1975.

    Google Scholar 

  18. J. van Leeuwen, The tape complexity of context-independent developmental languages,J. Computer and Systems Sciences 15, 203–211, 1975.

    Google Scholar 

  19. P. M. B. Vitányi, On the size of D0L languages, in Rozenberg, G. and Salomaa, A. (ed.)L Systems, Springer Lecture Notes in Computer Science 15, 72–77, 1974.

    Google Scholar 

  20. D. H. Younger, Recognition and parsing of context-free languages in Timen 3,Information and Control 10, 189–208, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jones, N.D., Skyum, S. Complexity of some problems concerningL systems. Math. Systems Theory 13, 29–43 (1979). https://doi.org/10.1007/BF01744286

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01744286

Keywords

Navigation