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In parallel computation two approaches are common; namely unbounded parallelism and bounded parallelism. In this paper both approaches will be considered. The problem of unbounded parallelism is studied in section II and some lower and upper bounds on different connectivity problems for directed and undirected graphs are presented. In section III we mention bounded parallelism and three different...
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The proof theory of structured programming insofar as concerned with flow of control is investigated. Various proof rules for the while, repeat-until and simple iteration statements - all essentially variants of Hoare's original while rule - are analyzed with respect to their soundness and adequacy. Next, a recently proposed proof rule for recursive procedures due to Dijkstra is - after correction...
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A model is defined in which questions concerning delay bounded asynchronous parallel systems may be investigated. Persistence and determinacy are introduced for this model. These two conditions are shown to be sufficient to guarantee that a synchronous execution policy can be relaxed to an asynchronous execution policy with no change to the result of the computation. In addition, the asynchronous...
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We show the existence of polynomials with 0-1 coefficients that are hard to evaluate even when arbitrary preconditioning is allowed. Further we show that there are power series with 0-1 coefficients such that their initial segments are hard to evaluate.
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In this paper, an investigation of the parallel arithmetic complexity of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix is reported. The parallel arithmetic complexity of solving equations has been an open question for several years. The gap between the complexity of the best algorithms (2n + 0(1), where n is the...
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We consider expressions whose arguments are relations and whose operators are chosen from among ∪, ο, *, and -1. We further assume that operands may be designated "sparse" or "dense", in a manner to be made formal subsequently. Our aim is to determine whether the evaluation of such an expression is (a) as hard as general transitive closure (b) as hard as transitive closure for...
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Given partially ordered sets (posets) P and Q, it is often useful to construct maps g:P→Q which are chain-continuous: least upper bounds (supremums) of nonempty linearly ordered subsets are preserved. Chaincontinuity is analogous to topological continuity and is generally much more difficult to verify than isotonicity: the preservation of the order relation. This paper introduces the concept of an...
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In this note we show that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation. We then use this result to show that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log n and log log n tape bounds. We also show that every infinite sla language recognizable on less than log n tape has infinitely...
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This paper considers simple LISP-like languages for the recursive definition of functions, focusing upon the connections between formal computation rules for calculation and the mathematical semantics of recursive definitions. A computation rule is correct when it is capable of computing the minimal fixpoint of a recursive definition. We give necessary and sufficient conditions for the correctness...
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We present a data structure, based upon a stratified binary tree, which enables us to manipulate on-line a priority queue whose priorities are selected from the interval 1...n, with an average and worst case processing time of O(log log n) per instruction. The structure is used to obtain a mergeable heap whose time requirements are about as good.
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It is shown that there is a sequence of languages E1, E2,... such that every correct prefix parser (one which detects errors at the earliest possible moment, e.g., LR or LL parsers) for En has size 2cn, yet a deterministic PDA recognizing En exists and has size O(n2). There is another easily described sequence of languages N1,N2,... for which Nn has a nondeterministic PDA of size O(n2) but no deterministic...
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To within a constant factor, only two complexity classes of complete binary bases exist. We show that they are separated by at most O(nlog310), or about O(n2.095), complementing a result of Khrapchenko that establishes an order n2 lower bound.
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In this paper Valiant's decision procedure for equivalence of deterministic finite-turn pushdown machines is improved upon. The improved equivalence test is: Given two mahcines, one constructs a pushdown machine that simulates them simultaneously and accepts a string iff it is accepted by exactly one of them. The given machines are equivalent iff the simulating pda accepts the empty language. The...
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We prove that an algorithm for selecting both the minimum and maximum element from an unordered set is minimean optimal. This algorithm had already been shown to be minimax optimal. The circumstances in which the same algorithm is optimum for both norms leads to a conjecture relating both norms. The method of proof utilizes a new idea in the theory of sorting optimality, namely degree information...
