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A certain modular representation of multilinear polynomials is considered. The modulo 6 representation of polynomial f is just any polynomial f + 6g. The 1-a-strong representation of f modulo 6 is polynomial f + 2g + 3h, where no two of g, f, and h have common monomials. Using this representation, some surprising applications are described: it is shown that n homogeneous linear polynomials x1,x2...
This paper addresses the problem of how to adapt an algorithm designed for fixed topology networks to produce the intended results, when run in a network whose topology changes dynamically, in spite of encountering topological changes during its execution. We present a simple and unified procedure, called a reset procedure, which, when combined with the static algorithm, achieves this adaptation....
The deadlock resolution problem can be informally stated as follows. There exists a set of actions, generated at different times, with some complex and contradictory precedence constraints between their executions. To resolve a deadlock, some of the actions need to be aborted; this enables to execute the remaining ones. This problem naturally arises in the context of distributed systems, e.g. communication...
We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.
We establish new upper bounds on the complexity of several "rectangle" problems. Our results include, for instance, optimal algorithms for range counting and rectangle searching in two dimensions. These involve linear space implementations of range trees and segment trees. The algorithms we give are simple and practical; they can be dynamized and taken into higher dimensions. Also of interest...
Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other. A particularly useful class of simplification orderings, the "recursive path orderings", is defined. Several examples of the use of such orderings...
A model for searching algorithms is developed which includes most tree-like searching structures such as lists, binary trees, AVL trees and 2, 3-trees. It is shown that no searching algorithm employing a data structure that is uniquely represented (up to isomorphism) can provide search, insert and delete functions all operating faster than c√n time for every n key tree. The c√n bound is shown to be...
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