On the Tape Complexity of Deterministic Context-Free Languages

Abstract

Let DSPACE(L(n)) denote the family of languages recognized by deterministic L(n)-tape bounded Turmg machines The pnnopal result described m this paper is the equivalence of the following statements (l) The determtmsttc context-free language L~ 2) (described m the paper) is m DSPACE(Iog(n)) (2) The simple LL(I) languages are m DSPACE(tog(n)) (3) The simple precedence languages are in DSPACE(Iog(n)). (4) DSPACE(Iog(n)) is identical to the famdy of languages recogmzed by deterministic two-way multlhead pushdown automata m polynomml tmae These results are obtained by constructing a determlmstlc context-free language L~ 2~ which is log(n)-complete for the family of determlmstlc context-free languages In other words, a tape hardest deterministic context-free language is described The best upper bound known on the tape complexity of (deterministic) context-free languages is (log(n)) 2. © 1978, ACM. All rights reserved.