Abstract
In this paper we present two results concerning the time and space complexity of context-free recognition. The first result states that cfl's can be recognized on a cube-connected computer (CCC) or on a perfect-shuffle computer (PSC) in log2n time using n6 processors. There are known algorithms with the same parallel time complexity but they use more powerful models of computation. The second result states that deterministic cfl's can be recognized in polynomial time using one log2n bounded pushdown store and log n tape. Known algorithms use log2n tape. Since algorithm is a simulation of a deterministic pda it may be looked upon as an efficient reduction of the height of the pushdown store. The second result is obtained by applying a transformation of a fast parallel recognition of deterministic cfl's and it can be viewed as an application of parallel algorithms to the design of efficient sequential algorithms.
Both results are aimed not at improving the known complexity bounds, but rather at showing that the same complexity can be obtained on less powerful models of computation.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
B.von Braunmuhl,R.Verbeek. A recognition algorithm for deterministic cfl's optimal in time and space. 21-st IEEE Symp. on Found. of Computer Science (1980)
B. von Braunmuhl,S. Cook,K. Mehlhorn,R. Verbeek. The recognition of deterministic cfl's in small time and space. Information and Control 56, pp.34–51 (1983)
S.A.Cook. Deterministic cfl's are accepted simultaneously in polynomial time and log squared space. 11-th ACM Symp. on Theory of computing (1979)
E.Dekel,D.Nassimi,S.Sahni. Parallel matrix and graph algorithms. SIAM Journal on Comp. 10 (4) (1981)
S.Fortune,J.Wyllie. Parallellism in random access machines. 10-th ACM Symp. on Theory of Comp. (1978)
J.Reif. Parallel time 0(log n) acceptance of deterministic cfl's 23-th IEEE Symp. on Found. of Comp. Science (1982)
W.L. Ruzzo. Tree-size bounded alternation. JCSS 21, pp. 218–235 (1980)
W.Rytter. Time complexity of two-way pushdown automata and recursive programs. NATO Adv. Research Workshop, Combinatorial algorithms on words(ed.A.Apostolico,Z.Galil) (1984) to appear in Springer-Verlag
W.Rytter. Parallel time 0(log n) recognition of unambiguous cfl's Proceedings FCT (1985)
W.Rytter,R.Giancarlo. Recognizing input-driven and parsing bracket languages on parallel machines. manuscript (1985)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rytter, W. (1985). On the recognition of context-free languages. In: Skowron, A. (eds) Computation Theory. SCT 1984. Lecture Notes in Computer Science, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16066-3_26
Download citation
DOI: https://doi.org/10.1007/3-540-16066-3_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16066-3
Online ISBN: 978-3-540-39748-9
eBook Packages: Springer Book Archive