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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.
Syntactic clues are aids to parsing. The amount of nondeterminism in parsers for pairs of homomorphically related semithue language systems is compared. If the parsers are without lookahead, the domain language system parser has no more nondeterminism than the codomain language system parser. The domain language system has at least as many clues. If the parsers have lookahead and the homomorphism...
Optimality, to within a multiplicative constant, is shown for some algorithms dealing with vectors and finite sets. Among the problems discussed are: Is vector x equal to vector y ? Given two finite sets A and B, is A = B ? Is A ⊆ B ? Is A ∩ B = φ ? What is |A ∩ B| ? What is |A - B| ? Is A - B = φ ?
We study the effect of program structure on computational efficiency in a class of abstract languages which model actual high-level numerical programming languages (like ALGOL). The results have bearing on programming technique (the use of go to statements), and they yield interesting facts about Blum's speed-up theorem for subrecursive computational complexity.
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