Abstract
We show that for any alphabet Σ there is a setL ∑ \( \subseteq\)∑* such that ifC is any infinite co-infinite context-free language over Σ, thenL Σ splitsC (i.e., each ofL ∑ ⋂C,L ∑ \(\bar C\),\(\overline {L_\Sigma }\)⋂C, and\(\overline {L_\Sigma }\)⋂\(\bar C\) is infinite).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Breidbart, On splitting recursive sets,J. Comput. System Sci., to appear.
S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.
J. C. Owings, Jr., Splitting a context-sensitive set,J. Comput. System Sci., 10, 83–87 (1975).
R. Parikh, On context-free languages,J. Assoc. Comput. Mach., 13, 570–581 (1966).
Author information
Authors and Affiliations
Additional information
Preparation of this paper was supported in part by the National Science Foundation under Grant No. MCS77-11360.
Rights and permissions
About this article
Cite this article
Breidbart, S. A short note on simultaneous splitting. Math. Systems Theory 12, 129–131 (1978). https://doi.org/10.1007/BF01776569
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01776569