Skip to main content
Springer Nature Link
Log in

A unified approach to the generation and the acception of formal languages

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

The duality of generation and acception of the Chomsky classes of languages is emphasized by considering the corresponding acceptors as Semi-Thue-Systems instead of unnatural “machines”.

It is shown as one main result that lba's, pda's and fsa's are characterized by imposing extremely simple and natural length conditions on the productions of the accepting Semi-Thue-System. As a second result, the shift-reduce or LR-acceptor which is wellknown from syntax analysis is generalised for CH-1 and CH-0 languages. As for contextfree languages, the LR-acceptor when scanning a word from Left to right yields a Right-most derivation in the general sense.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Büchi, J.R.: Regular canonical systems and finite automata. University of Michigan. Ann Arbor. Technical Report, 1959

    Google Scholar 

  2. Büchi, J.R.: Regular canonical systems. Arch. Math. Logik Grundlagenforsch. 6, 91–111 (1964)

    Google Scholar 

  3. Cannon, R.L.: State grammar parsing. PhD. Thesis, Univ. North Carolina. Chapel Hill, 1973

    Google Scholar 

  4. Deussen, P.: Strategies in acceptors and their relation 10 LR(k)-LL(k)-Theories. Interner Bericht Nr. 8 77. Fakultät für Informatik, Universität Karlsruhe, 1977

  5. Goos, G.: Überselzerbau. Manuscript (to be published)

  6. Hotz, G.: Eindeutigkeit und Mehrdeutigkeit formaler Sprachen. Elektron. Informationsverarb. Kybernetik 2. Heft 4, 235–246 (1966)

    Google Scholar 

  7. Hotz, G., Claus, V.: Automatentheorie und formale Sprachen. III. Formale Sprachen. BI, Hochschulskriptum, 1972

  8. Hopcroft, J.E., Ullman, J.D.: Formal languages and their relation to automata. Reading, Massachusetts: Addison-Wesley 1969

    Google Scholar 

  9. Kasai, T.: A hierarchy between context-free and context-sensitive languages. J. Comput. System Sci. 492–508 (1970)

  10. Langmaack, H.: Zur Äquivalenz der Hotzschen und Paulschen Definition der Mehrdeutigkeit von Chomsky-Sprachen. In: 4. Kolloquium über Automatentheorie, Erlangen, 1967

  11. Langmaack, H.: Application of regular canonical systems to grammars translatable from left to right. Acta Informat. 1, 115–138 (1971)

    Google Scholar 

  12. Langmaack, H., Eickel, J.: Präzisierung der Begriffe Phrasenstruktur und strukturelle Mehrdeutigkeit in Chomsky-Sprachen. In: 3. Kolloquium über Automatentheorie. Basel: Birkhäuser 1967

    Google Scholar 

  13. Langmaack, H., Schmidt, G.: Klassen unwesentlich verschiedener Ableitungen als Verbände. Tagungsbericht Automatentheorie und Formale Sprachen, BI, 1970

  14. Nelson, R.J.: Introduction to automata. New York: Wiley 1968

    Google Scholar 

  15. Salomaa, A.: Formal languages. New York: Academic Press 1973

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik I der Universität Karlsruhe, Postfach 6380, D-7500, Karlsruhe 1, Germany (Fed. Rep.)

    P. Deussen

Authors
  1. P. Deussen
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deussen, P. A unified approach to the generation and the acception of formal languages. Acta Informatica 9, 377–390 (1978). https://doi.org/10.1007/BF00289049

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289049

Keywords