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 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.