# On the recognition of context-free languages

## 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 log^{2}n time using n^{6} 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 log^{2}n bounded pushdown store and log n tape. Known algorithms use log^{2}n 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.

## References

- [1]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)Google Scholar
- [2]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)Google Scholar
- [3]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)Google Scholar
- [4]E.Dekel,D.Nassimi,S.Sahni. Parallel matrix and graph algorithms. SIAM Journal on Comp. 10 (4) (1981)Google Scholar
- [5]S.Fortune,J.Wyllie. Parallellism in random access machines. 10-th ACM Symp. on Theory of Comp. (1978)Google Scholar
- [6]J.Reif. Parallel time 0(log n) acceptance of deterministic cfl's 23-th IEEE Symp. on Found. of Comp. Science (1982)Google Scholar
- [7]W.L. Ruzzo. Tree-size bounded alternation. JCSS 21, pp. 218–235 (1980)Google Scholar
- [8]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-VerlagGoogle Scholar
- [9]W.Rytter. Parallel time 0(log n) recognition of unambiguous cfl's Proceedings FCT (1985)Google Scholar
- [10]W.Rytter,R.Giancarlo. Recognizing input-driven and parsing bracket languages on parallel machines. manuscript (1985)Google Scholar