Terminating Turing Machine Computations and the Complexity and/or decidability of Correspondence Problems, Grammars, and Program Schemes

Abstract

Three natural decision problems are presented: one for correspondence problems and linear context-free grammars, one for arbitrary context-free grammars, and one for program schemes. Each of these three decismn problems, although decidable, is shown to be of nonrecursive complexity. The complexities of these three decision problems are shown to easdy imply nonrecursive lower bounds on the complexities of wide classes of decision problems for their respective structures. As corollaries, a number of new nonrecursive lower complexity bounds, undecidabdRy results, and relative economy of descnptmn results are obtained for these structures. In addition, several decidable decision problems and effective procedures in the literature are shown to be of nonrecursive complexity. © 1984, ACM. All rights reserved.