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A characterization of alternating log time by first order functional programs
 In LPAR 2006, volume 4246 of LNAI
, 2006
"... Abstract. We a give an intrinsic characterization of the class of functions which are computable in NC 1 that is by a uniform, logarithmic depth and polynomial size family circuit. Recall that the class of functions in ALogTime, that is in logarithmic time on an Alternating Turing Machine, is NC 1. ..."
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Abstract. We a give an intrinsic characterization of the class of functions which are computable in NC 1 that is by a uniform, logarithmic depth and polynomial size family circuit. Recall that the class of functions in ALogTime, that is in logarithmic time on an Alternating Turing Machine, is NC 1. Our characterization is in terms of first order functional programming languages. We define measuretools called Supinterpretations, which allow to give space and time bounds and allow also to capture a lot of program schemas. This study is part of a research on static analysis in order to predict program resources. It is related to the notion of Quasiinterpretations and belongs to the implicit computational complexity line of research. 1
Derivational Complexity is an Invariant Cost Model ⋆
"... Abstract. We show that in the context of orthogonal term rewriting systems, derivational complexity is an invariant cost model, both in innermost and in outermost reduction. This has some interesting consequences for (asymptotic) complexity analysis, since many existing methodologies only guarantee ..."
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Cited by 3 (2 self)
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Abstract. We show that in the context of orthogonal term rewriting systems, derivational complexity is an invariant cost model, both in innermost and in outermost reduction. This has some interesting consequences for (asymptotic) complexity analysis, since many existing methodologies only guarantee bounded derivational complexity. 1
Quasifriendly supinterpretations
 in "8th International Workshop on Logic and Computational Complexity  LCC 2006  LICS affiliated Workshop, 10/08/2006, Seattle/EtatsUnis", James Royer
"... Abstract. In a previous paper [16], the supinterpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a supinterpretation provides an upper bound on the size of function outputs. In this forme ..."
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Abstract. In a previous paper [16], the supinterpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a supinterpretation provides an upper bound on the size of function outputs. In this former work, a criterion, which can be applied to terminating as well as nonterminating programs, was developed in order to bound polynomially the stack frame size. In this paper, we suggest a new criterion which captures more algorithms computing values polynomially bounded in the size of the inputs. Since this work is related to quasiinterpretations, we compare the two notions obtaining two main features. The first one is that, given a program, we have heuristics for finding a supinterpretation when we consider polynomials of bounded degree. The other one consists in the characterizations of the set of function computable in polynomial time and in polynomial space. 1
On QuasiInterpretations, Blind Abstractions and Implicit Complexity ∗
, 2006
"... Quasiinterpretations are a technique to guarantee complexity bounds on firstorder functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time ([14]), called here the Pcriterion. We study properties of the program ..."
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Quasiinterpretations are a technique to guarantee complexity bounds on firstorder functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time ([14]), called here the Pcriterion. We study properties of the programs satisfying the Pcriterion, in order to better understand its intensional expressive power. Given a program on binary lists, its blind abstraction is the nondeterministic program obtained by replacing lists by their lengths (natural numbers). A program is blindly polynomial if its blind abstraction terminates in polynomial time. We show that all programs satisfying a variant of the Pcriterion are in fact blindly polynomial. Then we give two extensions of the Pcriterion: one by relaxing the termination ordering condition, and the other one (the bounded value property) giving a necessary and sufficient condition for a program to be polynomial time executable, with memoisation. 1
Higherorder Interpretations and Program Complexity (Long Version)
, 2012
"... Polynomial interpretations and their generalizations like quasiinterpretations have been used in the setting of firstorder functional languages to design criteria ensuring statically some complexity bounds on programs [1]. This fits in the area of implicit computational complexity, which aims at g ..."
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Polynomial interpretations and their generalizations like quasiinterpretations have been used in the setting of firstorder functional languages to design criteria ensuring statically some complexity bounds on programs [1]. This fits in the area of implicit computational complexity, which aims at giving machinefree characterizations of complexity classes. Here we extend this approach to the higherorder setting. For that we consider the notion of simply typed term rewriting systems [2], we define higherorder polynomial interpretations (HOPI) for them and give a criterion based on HOPIs to ensure that a program can be executed in polynomial time. In order to obtain a criterion which is flexible enough to validate some interesting programs using higherorder primitives, we introduce a notion of polynomial quasiinterpretations, coupled with a simple termination criterion based on linear types and pathlike orders. 1
ProjectTeam CARTE Theoretical Adverse Computations, and Safety
"... c t i v it y e p o r t 2009 Table of contents ..."
Team CARTE Theoretical Adverse Computations, and Safety
"... c t i v it y e p o r t 2007 Table of contents ..."