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Foundations of Computer Science, 1975., 16th Annual Symposium on

Date 13-15 Oct. 1975

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Displaying Results 1 - 25 of 31
  • [Front cover]

    Publication Year: 1975 , Page(s): C1
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  • Table of contents

    Publication Year: 1975 , Page(s): iv - v
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  • Foreword

    Publication Year: 1975 , Page(s): iii
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  • The effect of the field of constants on the number of multiplications

    Publication Year: 1975 , Page(s): 1 - 2
    Cited by:  Papers (3)
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  • The exact time required to perform generalized addition

    Publication Year: 1975 , Page(s): 3 - 5
    Cited by:  Papers (1)
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  • Polynomials with 0-1 coefficients that are hard to evaluate

    Publication Year: 1975 , Page(s): 6 - 10
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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. View full abstract»

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  • Fast parallel matrix inversion algorithms

    Publication Year: 1975 , Page(s): 11 - 12
    Cited by:  Papers (2)
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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 number of unknowns/ equations) and the only proved lower bound (2 log n (All logarithms in this paper are of base two.)) was huge. The first breakthrough came when Csanky reported that the parallel arithmetic complexity of all these four problems has the same growth rate and exhibited an algorithm that computes these problems in 2n - O(log2n) steps. It will be shown in the sequel that the parallel arithmetic complexity of all these four problems is upper bounded by O(log2n) and the algorithms that establish this bound use a number of processors polynomial in n. This disproves I. Munro's conjecture. View full abstract»

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  • Parallel computations in graph theory

    Publication Year: 1975 , Page(s): 13 - 18
    Cited by:  Papers (1)
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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 k-parallel graph search techniques, namely k-depth search, breadth depth search, and breadth-first search. Each algorithm is analyzed with respect to the optimal serial algorithm. It is shown that for sufficiently dense graphs the parallel breadth first search technique is very close to the optimal bound. Techniques for searching sparse graphs are also discussed. View full abstract»

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  • Synchronization and computing capabilities of linear asynchronous structures

    Publication Year: 1975 , Page(s): 19 - 28
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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 execution time is only (D+1) times the synchronous execution time, where D is the delay bound. A wide class of recognition problems is identified which can be solved by linear asynchronous structures. Also, it is shown that synchronization problems, similar to the "firing squad synchronization problem," cannot be solved by delay bounded asynchronous systems. View full abstract»

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  • Flow of control in the proof theory of structured programming

    Publication Year: 1975 , Page(s): 29 - 33
    Cited by:  Papers (2)
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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 - shown to be a simple instance of Scott's induction rule. Finally, Manna & Pnueli's rule for total correctness of the while statement is formally justified using the Hitchcock & Park theory of program termination based on well-founded relations. View full abstract»

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  • Bases for chain-complete posets

    Publication Year: 1975 , Page(s): 34 - 47
    Cited by:  Papers (2)
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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 extension basis: a subset B of P such that any isotone f:B→Q has a unique chain-continuous extension g:P→Q. Two characterizations of the chain-complete posets which have extension bases are obtained. These results are then applied to the problem of constructing an extension basis for the poset [P→Q] of chain-continuous maps from P to Q, given extension bases for P and Q. This is not always possible, but it becomes possible when a mild (and independently motivated) restriction is imposed on either P or Q. A lattice structure is not needed. Finally, we consider extension bases which can be recursively listed and derive a recently established theorem as a corollary. View full abstract»

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  • Correct computation rules for recursive languages

    Publication Year: 1975 , Page(s): 48 - 56
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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 of rules under (a) all possible interpretations and (b) particular interpretations. View full abstract»

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  • On time versus space and related problems

    Publication Year: 1975 , Page(s): 57 - 64
    Cited by:  Papers (7)
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  • A note on tape bounds for sla language processing

    Publication Year: 1975 , Page(s): 65 - 70
    Cited by:  Papers (1)
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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 many different regular subsets, and, therefore, the set of primes in unary notation, P, requires exactly log n tape for its recognition and every infinite subset of P requires at least log n tape. View full abstract»

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  • Minimean optimality in sorting algorithms

    Publication Year: 1975 , Page(s): 71 - 74
    Cited by:  Papers (2)
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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 of the Hasse digraphs. View full abstract»

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  • Preserving order in a forest in less than logarithmic time

    Publication Year: 1975 , Page(s): 75 - 84
    Cited by:  Papers (6)
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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. View full abstract»

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  • On the complexity of comparison problems using linear functions

    Publication Year: 1975 , Page(s): 85 - 89
    Cited by:  Papers (4)
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  • Evaluating relational expressions with dense and sparse arguments

    Publication Year: 1975 , Page(s): 90 - 97
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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 sparse graphs. (c) as hard as connected components of an undirected graph. View full abstract»

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  • On the decision tree complexity of the shortest path problems

    Publication Year: 1975 , Page(s): 98 - 99
    Cited by:  Papers (1)
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  • An O (N2.5) algorithm for maximum matching in general graphs

    Publication Year: 1975 , Page(s): 100 - 112
    Cited by:  Papers (5)
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    This work presents a new efficient algorithm for finding a maximum matching in an arbitrary graph. Two implementations are suggested, the complexity of the first is O(n2.5) and the complexity of the second is O(m√n¿log n) where n, m are the numbers of the vertices and the edges in the graph. View full abstract»

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  • Information theory and the complexity of switching networks

    Publication Year: 1975 , Page(s): 113 - 118
    Cited by:  Papers (1)
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  • The effect of basis on size of Boolean expressions

    Publication Year: 1975 , Page(s): 119 - 121
    Cited by:  Papers (1)
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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. View full abstract»

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  • Economy of description by parsers, DPDA's, and PDA's

    Publication Year: 1975 , Page(s): 122 - 127
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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 PDA of size less than 2cn. It is shown moreover, that this latter exponential gap can be made arbitrarily large for different sequences of languages. View full abstract»

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  • An improvement on valiant's decision procedure for equivalence of deterministic finite-turn pushdown automata

    Publication Year: 1975 , Page(s): 128 - 134
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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 simulating machine uses its pushdown store to hold the contents of the stores of the two simulated machines. In order ot prevent the tops of the two stores to get too far apart the simulating machine sometimes replaces the contents of one of the stores. Valiant 1,2 has proved the existence of a suitable function which determines the replacements. The crux of this paper is an algorithm for constructing such a function. The existence of such an algorithm enables us to calculate an upper bound on the time complexity of the improved algorithm. We obtain the results that equivalence of deterministic finite-turn pushdown automata can be tested in super-exponential time and equivalence of deterministic two-tape automata can be tested in exponential time. View full abstract»

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  • A grammatical characterization of exponential-time languages

    Publication Year: 1975 , Page(s): 135 - 143
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    We show that the languages generated by a constrained form of Chomsky's transformational grammars characterize the languages recognized by Turing machines in deterministic exponential (2cn) time. The constraints on the transformational grammars are satisfied by many, though not all, known grammars in linguistic practice. We also give a simple algebraic characterization of the same class of languages and use it for the linguistic characterization. View full abstract»

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