On Lexicographic Termination Ordering with Space Bound Certifications

Bonfante, Guillaume; Marion, Jean-Yves

doi:10.1007/3-540-45575-2_46

Cited by 27 publications

(40 citation statements)

References 15 publications

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“…The specific conditions on constructors correspond to the notion of kind 0 quasi-interpretation presented in [BMM01]. However, we work over the non-negative rationals rather than over the natural numbers and we force the interpretation 0 for constants.…”

Section: Quasi-interpretationsmentioning

confidence: 99%

“…Quasi-interpretations can be combined with various methods enforcing program termination. In particular, in [BMM01] it is shown that a program terminating by lexicographic path-order (lpo 6 ) and admitting a polynomially bounded quasiinterpretation (polynomial in the usual sense) can be evaluated in Pspace. For a lower bound, we refer to the encoding of quantified boolean formulas (qbf) in appendix A that terminates by lpo and admits a multi-linear max-plus quasi-interpretation.…”

Section: Lower and Upper Bounds On Complexitymentioning

confidence: 99%

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Max-Plus Quasi-interpretations

Amadio

2003

Lecture Notes in Computer Science

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Abstract/RésuméQuasi-interpretations are a tool to bound the size of the values computed by a first-order functional program (or a term rewriting system) and thus a mean to extract bounds on its computational complexity. We study the synthesis of quasi-interpretations selected in the space of polynomials over the max-plus algebra determined by the non-negative rationals extended with −∞ and equipped with binary operations for the maximum and the addition. We prove that in this case the synthesis problem is NP-hard, and in NP for the particular case of multi-linear quasi-interpretations when programs are specified by rules of bounded size.The relevance of multi-linear quasi-interpretations is discussed by comparison to certain syntactic and type theoretic conditions proposed in the literature to control time and space complexity.Keywords: Functional languages and term rewriting. Function algebras and implicit computational complexity. Static analysis. Polynomial interpretations and max-plus algebras.Les quasi-interprétations sont un outil pour borner la taille des valeurs calculées par un programme fonctionnel du premier ordre (ou un système de réécriture de termes) et ainsi un moyen pour extraire des bornes sur sa complexité. Nousétudions la synthése des polynômes sur l'algèbre max-plus determinée par le rationnels non-negatifsétendus avec −∞. Nous demontrons que dans ce cas le problème de la synthèse est NP-difficile et dans NP pour le cas particulier des quasi-interpretations multi-linéaires quand les programmes sont specifiés par des règles de taille bornée. L'intérêt des quasi-interprétation multi-linéaires est discuté par comparaisoǹ a certaines restrictions syntaxiques et de typage proposées dans la litterature pour contrôler la complexité en temps et en espace.

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Section: Quasi-interpretationsmentioning

confidence: 99%

Section: Lower and Upper Bounds On Complexitymentioning

confidence: 99%

Max-Plus Quasi-interpretations

Amadio

2003

Lecture Notes in Computer Science

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“…There is a large collection of static analysis techniques (see, e.g., [11,7,12,13,14,9] that allow to establish feasible reactivity of functional programs. A common feature of these methods is the combination of traditional termination methods with what could be called a data-size flow analysis.…”

Section: Introductionmentioning

confidence: 99%

“…First of all, we have to find an abstract way to describe the data-size flow of a program. To this end, we import and adapt the concept of quasi-interpretation that has been proposed in the context of the analysis of the computational complexity of first-order functional programs [9,4]. As a second step, we describe a method to associate with a program a finite set of inequalities on first-order terms and prove that whenever these inequalities are satisfied by a (polynomially bounded) quasi-interpretation the program is feasibly reactive.…”

Section: Introductionmentioning

confidence: 99%

Feasible reactivity in a synchronous Π-calculus

Amadio

Dabrowski

2007

Proceedings of the 9th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

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Reactivity is an essential property of a synchronous program. Informally, it guarantees that at each instant the program fed with an input will 'react' producing an output. In the present work, we consider a refined property that we call feasible reactivity. Beyond reactivity, this property guarantees that at each instant both the size of the program and its reaction time are bounded by a polynomial in the size of the parameters at the beginning of the computation and the size of the largest input. We propose a method to annotate programs and we develop related static analysis techniques that guarantee feasible reactivity for programs expressed in the Sπ-calculus. The latter is a synchronous version of the π-calculus based on the SL synchronous programming model. IntroductionMastering the computational complexity of programs is an important aspect of computer security with applications ranging from embedded systems to mobile code and smartcards. One approach to this problem is to monitor at run time the resource consumption and to rise an exception when some bound is reached. A variant of this approach is to instrument the code so that bounds are checked at appropriate time. An alternative approach is to analyse statically the program to guarantee that during the execution it will respect certain resource bounds. In other words, the first approach performs a dynamic verification while the second relies on a static analysis. As usual, the main advantage of the first approach is its flexibility while the advantage of the second approach is the fact that it does not introduce an overhead at run time and, perhaps more importantly, that it allows an early detection of 'buggy' programs. In this work, we will focus on the static analyses which offer the more challenging problems while keeping in mind that the two approaches are complementary. For instance, static analyses may be helpful in reducing the frequency of dynamic verifications. *

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“…It was demonstrated in [1,8] that the synthesis problem is decidable in exponential time for small classes of polynomials. Quasi-interpretations and sup-interpretations have already been used to capture the sets of functions computable in polynomial time and space [26,7] and capture a broad class of algorithms, including greedy algorithms and dynamic programming algorithms. Consequently, it is a challenge to study whether this approach can be adapted to characterize small parallel complexity classes.…”

Section: Introductionmentioning

confidence: 99%

A Characterization of NC k by First Order Functional Programs

Marion

Péchoux

Lecture Notes in Computer Science

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Abstract. This paper is part of a research on static analysis in order to predict program resources and belongs to the implicit computational complexity line of research. It presents intrinsic characterizations of the classes of functions, which are computable in NC k , that is by a uniform, poly-logarithmic depth and polynomial size family of circuits, using first order functional programs. Our characterizations are new in terms of first order functional programming language and extend the characterization of NC 1 in [9]. These characterizations are obtained using a complexity measure, the sup-interpretation, which gives upper bounds on the size of computed values and captures a lot of program schemas.

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On Lexicographic Termination Ordering with Space Bound Certifications

Cited by 27 publications

References 15 publications

Max-Plus Quasi-interpretations

Max-Plus Quasi-interpretations

Feasible reactivity in a synchronous Π-calculus

A Characterization of NC k by First Order Functional Programs

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