Abstract
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 ≔ {x n¯x n¦ n ∈ N ⊂D ′*1 is used for this cancellation, then each recursively enumerable set can be obtained from linear context-free languages.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
M. Benois: Parties rationelles du groupe libre. C. R. Acad. Sc. Paris, Ser. A t. 269 (1969) 1188–1190.
R.V. Book, M. Jantzen, C. Wrathall: Monadic Thue systems. Theoret. Comput. Sci. 19 (1982) 231–251.
F.J. Brandenburg: Cancellations in linear context-free languages. Techn. report MIP-8904, Univ. Passau (1989).
F.J. Brandenburg, J. Dassow: Reductions of picture words. Techn. report MIP-8905, Univ. Passau (1989).
Ch. Frougny, J. Sakarovitch, P. Schupp: Finiteness conditions on subgroups and formal language theory. Proc. London Math. Soc. 58 (1989) 74–88.
V. Geffert: Grammars with context dependency restricted to synchronization. LNCS vol. 233, Springer-Verlag (1986) 370–378.
S.A. Greibach: Full AFLs and nested iterated substitution. Inf. Contr. 16 (1970) 7–35.
T.V. Griffiths: Some remarks on derivations in general rewriting systems. Inform. Control 12 (1968) 27–45.
M. Hack: Petri net languages. C.S.G. Memo 124, Project MAC, MIT (1975).
M. Jantzen: Confluent string rewriting. EATCS Monographs 14, Springer-Verlag (1988).
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.
M. Jantzen, M. Kudlek, K.-J. Lange, H. Petersen: Dyck 1-reductions of context-free languages. Comp. and Artificial Intelligence, 9 (1990) 3–18.
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.
T. Kimura: Formal description of communication behaviour. Proc. Johns Hopkins Conf. on Information Sciences and Systems (1979).
H.A. Maurer, A. Salomaa, D. Wood: A Supernormal-Form Theorem for Context-Free Grammars. JACM 30 (1983) 95–102.
W.J. Savitch: How to make arbitrary grammars look like context-free grammars. SIAM J. Comput. 2 (1973) 174–182.
W.J. Savitch: Some characterizations of Lindenmayer systems in terms of Chomsky-type grammars and stack machines. Inf. Contr. 27 (1975) 37–60.
W.J. Savitch: Parenthesis grammars and Lindenmayer sytems. In: G. Rozenberg, A. Salomaa (eds.): The Book of L, Springer-Verlag (1986) 403–411.
D. Stanat: Formal languages and power series. 3rd ACM Sympos. Theory of Computing (1971) 1–11.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jantzen, M., Petersen, H. (1993). Cancellation in context-free languages: Enrichment by reduction. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_23
Download citation
DOI: https://doi.org/10.1007/3-540-56503-5_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56503-1
Online ISBN: 978-3-540-47574-3
eBook Packages: Springer Book Archive