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13th Annual Symposium on Switching and Automata Theory (swat 1972)

25-27 Oct. 1972

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  • [Front cover]

    Publication Year: 1972, Page(s): C1
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    Freely Available from IEEE
  • Table of contents

    Publication Year: 1972, Page(s):4 - 5
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    Freely Available from IEEE
  • Foreword

    Publication Year: 1972, Page(s): 3
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    Freely Available from IEEE
  • Program equivalence and context-free grammars

    Publication Year: 1972, Page(s):7 - 18
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (781 KB)

    This note defines a new equivalence relation among systems of recursion equations and a method for assigning context-free grammars to these systems, such that (1) The new equivalence implies strong equivalence; (2) Systems are equivalent in the new sense iff their grammars generate the same language; (3) There is a nontrivial decidable class of systems whose grammars have the decidability properti... View full abstract»

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  • Effective computability in algebraic structures

    Publication Year: 1972, Page(s):19 - 26
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  • Representing program schemes in logic

    Publication Year: 1972, Page(s):27 - 39
    Cited by:  Papers (1)
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    Our principle technical results are the development of a family of first order logics (called FILs), the translation of classes of program schemes into these logics and the development of routine decision procedures for these representations. We feel the results are interesting because the class of schemes include a previously studied important class (Paterson's monadic non-intersecting loops clas... View full abstract»

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  • SGML results in computational topology

    Publication Year: 1972, Page(s):40 - 51
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    It is the object of this paper to study the topological properties of finite graphs that can be imbedded in the n-dimensional integral lattice (denoted Nn). The basic notion of deletability of a node is first introduced. A node is deletable with respect to a graph if certain computable conditions are satisfied on its neighborhood. An equivalence relation on graphs called reducibility and denoted b... View full abstract»

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  • On homomorphisms, simulations, correctness and subroutines for programs and program schemes

    Publication Year: 1972, Page(s):52 - 60
    Cited by:  Papers (2)
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  • Honest bounds for complexity classes of recursive functions

    Publication Year: 1972, Page(s):61 - 66
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    A new simplified proof of the McCreight-Meyer Honesty or Naming Theorem is given. Let t be a recursive function, and let F(t) be the set of recursive function computable within time bound t. Then it is shown that an honest recursive t′ can be found which is arbitrarily large on a dense set of arguments such that F(t) = F(t′). View full abstract»

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  • Renamings in program schemas

    Publication Year: 1972, Page(s):67 - 70
    Cited by:  Papers (2)
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  • Consistency of synchronization nets using P and V operations

    Publication Year: 1972, Page(s):71 - 77
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    In this paper we provide a formulation of the synchronized execution of a system of tasks using generalized P and V operations. We explore the properties of such processes and present as a main result a decision procedure for settling the consistency question. View full abstract»

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  • On the decomposition of asynchronous systems

    Publication Year: 1972, Page(s):78 - 89
    Cited by:  Papers (1)
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    This paper reports of part of a contunuing investigation of parallel computation, in particular, efforts toward understanding the nature of different types of parallel control. The first section defines an asynchornous system to be a simple type of state machine. This was arrived at in an attempt to generalize from the types of control in parallel program schemata and networks of asynchronous modu... View full abstract»

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  • Fast modular transforms via division

    Publication Year: 1972, Page(s):90 - 96
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (607 KB)

    It is shown that the problem of evaluating an Nth degree polynomial is reducible to the problem of dividing the polynomial. A method for dividing an Nth degree polynomial by an N/2 degree polynomial in O(N log 2N) steps is given. Using this it is shown that the evaluation of an Nth degree polynomial at N points can be done in O(N log 3N). The related problem of computing of computing the resides o... View full abstract»

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  • The efficient calculation of powers of polynomials

    Publication Year: 1972, Page(s):97 - 104
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (731 KB)

    Suppose we are given a polynomial in (X1,..., Xr) in r ≥ 1 variables, let m bound the degree of p in all variables Xi, 1≤i≤r, and we wish to raise P to the nth power, n≫1. In a recent paper which compared the iterative versus the binary method it was shown that their respective computing times were O(m2rnr+1) versus O((mn) 2r) when using single precision arithmetic. ... View full abstract»

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  • On the number of multiplications for the evaluation of a polynomial and all its derivatives

    Publication Year: 1972, Page(s):105 - 107
    Cited by:  Papers (1)
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  • On the relation of graph grammars and graph automata

    Publication Year: 1972, Page(s):108 - 120
    Cited by:  Papers (3)
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    It is shown that a strong relationship exists between sets of graphs defined by graph (walking) automata with markers available and sets defined by graph grammars. Polynomial recognition algorithms are presented for certain classes of sets and it is argued that the existence of polynomial algorithms for other classes is doubtful. Other properties of the classes of sets defined by graph automata an... View full abstract»

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  • The emptiness problem for automata on infinite trees

    Publication Year: 1972, Page(s):121 - 124
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (453 KB)

    The purpose of this paper is to give an alternative proof to the decidability of the emptiness problem for tree automata, as shown in Rabin4. The proof reduces the emptiness problem for automata on infinite trees to that for automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitely-generable tree. View full abstract»

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  • The equivalence problem for regular expressions with squaring requires exponential space

    Publication Year: 1972, Page(s):125 - 129
    Cited by:  Papers (81)
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  • Some related problems from network flows, game theory and integer programming

    Publication Year: 1972, Page(s):130 - 138
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (833 KB)

    We consider several important problems for which no polynomially time bounded algorithm is known. These problems are shown to be related in that a polynomial algorithm for one implies a polynomial algorithm for the others. View full abstract»

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  • Some results on the effect of arithmetics on comparison problems

    Publication Year: 1972, Page(s):139 - 143
    Cited by:  Papers (8)
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  • Fast allocation algorithms

    Publication Year: 1972, Page(s):144 - 154
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1507 KB)

    In this paper we consider polynomial-time algorithms for bin packing and their applications. The previously studied FIRST FIT and BEST FIT algorithms are shown to be special cases of a more generalized class of algorithms which all have similar worst case behavior. Linear time algorithms are then introduced which, though "faster" than FIRST FIT and BEST FIT, have the same, or better, worst case be... View full abstract»

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  • Optimal scheduling on multi-processor computing systems

    Publication Year: 1972, Page(s):155 - 160
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (581 KB)

    A set of tasks {T1, T2, ..., Tr] are to be scheduled on a two-processor computing system. The execution time of each of the tasks is given. Moreover, a partial ordering ≪ over the set of tasks is specified. If Ti ≪ Tj, it is required that the execution of Tj will not begin until the completion of the execution of Ti. Let ω denote the total elapsed time for the execution of all... View full abstract»

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  • A fast algorithm for the elimination of common subexpressions

    Publication Year: 1972, Page(s):161 - 176
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    There is a class of flow charts called "reducible" for which many global code optimization algorithms have been recently written. As a practical matter, one may expect the flow chart of a program appearing "in nature" to be reducible with a probability over 90% [3], and those that are not can be made reducible by "node splitting" [10]. Unfortunately, the algorithms written for reducible grap... View full abstract»

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  • Universal test sets for logic networks

    Publication Year: 1972, Page(s):177 - 184
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (989 KB)

    This paper examines the problem of finding a single universal test set that will test any of a variety of different implementations of a given switching function. It is shown that, for and/or networks, universal test sets may be found which detect not only all single faults but all multiple faults as well. The minimality and size of these sets are examined and their derivation for incomplete and m... View full abstract»

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  • Multiple faults in Reed-Muller canonic networks

    Publication Year: 1972, Page(s):185 - 191
    Cited by:  Papers (2)
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    Fault detecting test sets to detect multiple stuck-at-faults in certain networks realizing Reed-Muller canonic expressions are given. It is shown that to detect t faults, t ≥ 1, in a network realizing an arbitrary n-variable logic function only 4 + Σ i=1 [log22t] (in) tests need be applied ([x] is the integer part of x) and that these tests are independent of the function being real... View full abstract»

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