A simplified lower bound for context-free-language recognition

Abstract

For on-line recognition of the words in an arbitrary linear context-free language, there are known tight bounds on the time required by a deterministic multitape Turing machine. In terms of word length n, the time need never be worse than some constant times n², even if only one worktape is available; and there is a linear context-free language that requires at least time proportional to n²/log n, no matter how many worktapes are available. Using Kolmogorov's notion of descriptional complexity as a tool, we present a simple proof of the latter result.