Cancellation in context-free languages: Enrichment by reduction

  • M. Jantzen
  • H. Petersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


The following problem is shown to be decidable: Given a context-free grammar G and a string w ∈ X*, does there exist a string u ∈ L(G) such that w is obtained from u by deleting all substrings u i , that are elements of the symmetric Dyck set D 1 * ?

The intersection of any two context-free languages can be obtained from only one context-free language by cancellation either with the smaller semi-Dyck set D 1 ′* D 1 * or with D 1 * itself.

Also, the following is shown here for the first time: If the set EQ ≔ {xn¯xn¦ n ∈ND 1 ′* is used for this cancellation, then each recursively enumerable set can be obtained from linear context-free languages.


Sentential Form Terminal Symbol Formal Language Theory Nonterminal Symbol Counter Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Benois: Parties rationelles du groupe libre. C. R. Acad. Sc. Paris, Ser. A t. 269 (1969) 1188–1190.Google Scholar
  2. [2]
    R.V. Book, M. Jantzen, C. Wrathall: Monadic Thue systems. Theoret. Comput. Sci. 19 (1982) 231–251.Google Scholar
  3. [3]
    F.J. Brandenburg: Cancellations in linear context-free languages. Techn. report MIP-8904, Univ. Passau (1989).Google Scholar
  4. [4]
    F.J. Brandenburg, J. Dassow: Reductions of picture words. Techn. report MIP-8905, Univ. Passau (1989).Google Scholar
  5. [5]
    Ch. Frougny, J. Sakarovitch, P. Schupp: Finiteness conditions on subgroups and formal language theory. Proc. London Math. Soc. 58 (1989) 74–88.Google Scholar
  6. [6]
    V. Geffert: Grammars with context dependency restricted to synchronization. LNCS vol. 233, Springer-Verlag (1986) 370–378.Google Scholar
  7. [7]
    S.A. Greibach: Full AFLs and nested iterated substitution. Inf. Contr. 16 (1970) 7–35.Google Scholar
  8. [8]
    T.V. Griffiths: Some remarks on derivations in general rewriting systems. Inform. Control 12 (1968) 27–45.Google Scholar
  9. [9]
    M. Hack: Petri net languages. C.S.G. Memo 124, Project MAC, MIT (1975).Google Scholar
  10. [10]
    M. Jantzen: Confluent string rewriting. EATCS Monographs 14, Springer-Verlag (1988).Google Scholar
  11. [11]
    M. Jantzen, H. Petersen: Petri net languages and one-sided Dyck1-reductions of context-free sets. in K. Voss, H. Genrich, G. Rozenberg (eds.): Concurrency and nets. Springer-Verlag (1987) 245–252.Google Scholar
  12. [12]
    M. Jantzen, M. Kudlek, K.-J. Lange, H. Petersen: Dyck 1-reductions of context-free languages. Comp. and Artificial Intelligence, 9 (1990) 3–18.Google Scholar
  13. [13]
    M. Jantzen, H. Petersen: Twisting Petri net languages and how to obtain them by reducing linear context-free sets. In: Proc. 12th Intern. Conf. on Petri nets, Gjern (1991) 228–236.Google Scholar
  14. [14]
    T. Kimura: Formal description of communication behaviour. Proc. Johns Hopkins Conf. on Information Sciences and Systems (1979).Google Scholar
  15. [15]
    H.A. Maurer, A. Salomaa, D. Wood: A Supernormal-Form Theorem for Context-Free Grammars. JACM 30 (1983) 95–102.Google Scholar
  16. [16]
    W.J. Savitch: How to make arbitrary grammars look like context-free grammars. SIAM J. Comput. 2 (1973) 174–182.Google Scholar
  17. [17]
    W.J. Savitch: Some characterizations of Lindenmayer systems in terms of Chomsky-type grammars and stack machines. Inf. Contr. 27 (1975) 37–60.Google Scholar
  18. [18]
    W.J. Savitch: Parenthesis grammars and Lindenmayer sytems. In: G. Rozenberg, A. Salomaa (eds.): The Book of L, Springer-Verlag (1986) 403–411.Google Scholar
  19. [19]
    D. Stanat: Formal languages and power series. 3rd ACM Sympos. Theory of Computing (1971) 1–11.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • M. Jantzen
    • 1
  • H. Petersen
    • 1
  1. 1.Fachbereich InformatikUniversität HamburgGermany

Personalised recommendations