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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 ?
The aim of this paper is not the establishment of new results, but the understanding, from a machine theoretic point of view, of results originally arrived at by algebraic means. A new criterion for series parallel irreducibility is given which makes no reference to underlying semigroups but involves only series parallel operations. Also, the irreducibility of prime counter machines is established...
La représentation matricielle minimale attachée à une série rationnelle en variables non commutatives permet de généraliser à ces séries des résultats connus en théorie des langages. Les méthodes employées permettent aussi d'étudier les parties rationnelles de certains monoïdes comme le groupe libre.
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.
The notion of context-free LR(K) and LL(K) grammars and of the related bottom-up and top-down syntax-directed parsings are well known [1,2,3]. In this report we present a number of synthesis algorithms which take a non-self-embedding, sequential, context-free grammar and produce the finite state transducer which either top-down or bottom-up parses sentences in the language induced by the grammar if...
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