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Polyranking for Polynomial Loops
, 2005
"... Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. We propose polyranking functions as a generalization of ranking functions for analyzing termination of loops. We de ..."
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Cited by 1 (0 self)
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Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. We propose polyranking functions as a generalization of ranking functions for analyzing termination of loops. We
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
 In International Symposium on Symbolic and Algebraic Computation 2004 (ISSAC04
, 2004
"... This paper presents the algebraic foundation for an approach for generating polynomial loop invariants in imperative programs. It is first shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Using this connection, a procedure for finding loop invaria ..."
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Cited by 34 (6 self)
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This paper presents the algebraic foundation for an approach for generating polynomial loop invariants in imperative programs. It is first shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Using this connection, a procedure for finding loop
Automatic Generation of Polynomial Loop Invariants for Imperative Programs
, 2003
"... A general framework is presented for automating the discovery of loop invariants for imperative programs. Theoretical results about the correctness and completeness of the proposed method are given. More importantly, it is shown how this abstract approach can be used to automatically infer polynomi ..."
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polynomial invariants. The method has been implemented in Maple. Evidence of its practical interest is shown by means of several nontrivial examples, for which the polynomial loop invariants generated are directly applicable for proving correctness by means of a simple verifier.
TestBased Inference of Polynomial LoopBound Functions
, 2010
"... This paper presents an interpolationbased method of inferring arbitrary degree loopbound functions for Java programs. Given a loop, by its “loopbound function ” we mean a function with the numeric program variables as its parameters, that is used to bound the number of loopiterations. Using our ..."
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Cited by 9 (4 self)
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analysis, loopbound functions that are polynomials with natural, rational or real coefficients can be found. Analysis of loop bounds is important in several different areas, including worstcase execution time (WCET) and heap consumption analysis, optimising compilers and terminationanalysis. While
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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–117]. This construction is substantially more complicated than the corresponding construction for classical Turing machines (TMs); in fact, even simple primitives such as looping, branching, and composition are not straightforward in the context of quantum Turing machines. We establish how these familiar primitives can
Maximizing Loop Parallelism and Improving Data Locality via Loop Fusion and Distribution
 IN LANGUAGES AND COMPILERS FOR PARALLEL COMPUTING
, 1994
"... Loop fusion is a program transformation that merges multiple loops into one. It is effective for reducing the synchronization overhead of parallel loops and for improving data locality. This paper presents three results for fusion: (1) a new algorithm for fusing a collection of parallel and seq ..."
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Cited by 148 (12 self)
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and sequential loops, minimizing parallel loop synchronization while maximizing parallelism; (2) a proof that performing fusion to maximize data locality is NPhard; and (3) two polynomialtime algorithms for improving data locality. These techniques also apply to loop distribution, which is shown
Polynomial Structures in OneLoop Amplitudes
, 803
"... Abstract: A general oneloop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from treelevel input in a twostep process. First, use known formulas to write the coefficients of (4 −2ǫ)dimensional master integrals; these for ..."
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Abstract: A general oneloop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from treelevel input in a twostep process. First, use known formulas to write the coefficients of (4 −2ǫ)dimensional master integrals
Generating All Polynomial Invariants in Simple Loops
, 2007
"... This paper presents a method for automatically generating all polynomial invariants in simple loops. It is rst shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Based on this connection, a xpoint procedure using operations on ideals and Grobner bas ..."
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Cited by 25 (2 self)
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This paper presents a method for automatically generating all polynomial invariants in simple loops. It is rst shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Based on this connection, a xpoint procedure using operations on ideals and Grobner
Termination of polynomial programs
 In VMCAI’2005: Verification, Model Checking, and Abstract Interpretation, volume 3385 of LNCS
, 2005
"... Abstract. We present a technique to prove termination of multipath polynomial programs, an expressive class of loops that enables practical code abstraction and analysis. The technique is based on finite differences of expressions over transition systems. Although no complete method exists for deter ..."
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Cited by 66 (4 self)
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Abstract. We present a technique to prove termination of multipath polynomial programs, an expressive class of loops that enables practical code abstraction and analysis. The technique is based on finite differences of expressions over transition systems. Although no complete method exists
Counting Solutions to Linear and Nonlinear Constraints through Ehrhart Polynomials: Applications to Analyze and Transform Scientific Programs
, 1996
"... In order to produce efficient parallel programs, optimizing compilers need to include an analysis of the initial sequential code. When analyzing loops with affine loop bounds, many computations are relevant to the same general problem: counting the number of integer solutions of selected free variab ..."
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Cited by 105 (0 self)
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In order to produce efficient parallel programs, optimizing compilers need to include an analysis of the initial sequential code. When analyzing loops with affine loop bounds, many computations are relevant to the same general problem: counting the number of integer solutions of selected free
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