This paper studies the complexity of the reachability problem (a typical and practically important instance of the model-checking problem) for simply-typed call-by-value programs with recursion, Boolean values, and non-deterministic branch, and proves the following results. (1) The reachability problem for order-3 programs is nonelementary. Thus, unlike in the call-by-name case, the order of the input program does not serve as a good measure of the complexity. (2) Instead, the depth of types is an appropriate measure: the reachability problem for depth-n programs is n-EXPTIME complete. In particular, the previous upper bound given by the CPS translation is not tight. The algorithm used to prove the upper bound result is based on a novel intersection type system, which we believe is of independent interest.
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