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Deterministic exponential lower time bounds are obtained for analyzing monadic recursion schemes, multi-variable recursion schemes, and recursive programs. The lower bound for multivariable recursion schemes holds for any domain of interpretation with at least two elements. The lower bound for recursive programs holds for any recursive programming language with a nontrivial predicate test (i.e. a...
We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to proofs of algebraic summation identities....
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
In order to obtain a short fault-detection sequence for a sequential machine, the concept of an easily testable machine is introduced. Such a machine is one which possesses a minimal-length homogeneous distinguishing sequence and requires no transfer sequences in the fault-detection sequence. A design procedure is presented in which an arbitrary machine is embedded in an easily testable machine by...
It is an open problem, suggested by Papert and McNaughton, to find a decision procedure for determining whether a regular event is locally testable. In this paper we provide a partial solution, giving two effectively decidable conditions, one necessary and one sufficient, for local testability. Our proofs are for the most part algebraic, using machine decompositions and semigroup theory.
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