Semantic Evaluation, Intersection Types and Complexity of Simply Typed Lambda Calculus

Kazushige Terui
Consider the following problem: given a simply typed lambda term of Boolean type and of order r, does it normalize to "true"? A related problem is: given a term M of word type and of order r together with a finite automaton D, does D accept the word represented by the normal form of M? We prove that these problems are n-EXPTIME complete for r=2n+2, and n-EXPSPACE complete for r=2n+3. While the hardness part is...