Computation models and function algebras

Clote, Peter

doi:10.1007/3-540-60178-3_81

Cited by 41 publications

(69 citation statements)

References 61 publications

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“…Such characterizations include descriptive characterization based on finite model theory like Fagin [Fag74], characterization by function algebra like [Cob62], or by combining both kinds of characterization like in [Gur83,Saz80]: see [Clo95,Imm99,EF95] for more complete references.…”

Section: Introductionmentioning

confidence: 99%

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Bournez

Cucker

Naurois

et al. 2003

Lecture Notes in Computer Science

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Abstract. We provide several machine-independent characterizations of deterministic complexity classes in the model of computation proposed by L. Blum, M. Shub and S. Smale. We provide a characterization of partial recursive functions over any arbitrary structure. We show that polynomial time computable functions over any arbitrary structure can be characterized in term of safe recursive functions. We show that polynomial parallel time decision problems over any arbitrary structure can be characterized in terms of safe recursive functions with substitutions.

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Section: Introductionmentioning

confidence: 99%

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Bournez

Cucker

Naurois

et al. 2003

Lecture Notes in Computer Science

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“…Following Bellantoni and Cook, a number of authors obtained programming languages by constraints on recursion, and under a plethora of names (e.g., safe, tiered or ramified recursion, see [5,18] for overviews), and this area continues to be active. The main difference with our work is that we consider full recursion in all variables, but place syntactic constraints on the function bodies (both cons-freeness and unitary variables).…”

Section: Related Workmentioning

confidence: 99%

The Power of Non-determinism in Higher-Order Implicit Complexity

Kop

Simonsen

2017

Programming Languages and Systems

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Abstract. We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack.While cons-free programs have previously been used by several authors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order 0. Previous work has shown that adding explicit non-determinism to consfree programs taking data of order 0 does not increase expressivity; we prove that this-dramatically-is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows for a characterisation of the entire class of elementary-time decidable sets.Finally we show how, even with non-deterministic choice, the original hierarchy of characterisations is restored by imposing different restrictions.

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“…In a fundamental perspective one is interested in providing functional algebras characterizations of small complexity classes (see [Clo95] for a survey). Cobham's characterization of polynomial time by bounded recursion on notation [Cob65] is an early example.…”

Section: Motivationsmentioning

confidence: 99%

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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Computation models and function algebras

Cited by 41 publications

References 61 publications

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

The Power of Non-determinism in Higher-Order Implicit Complexity

Max-Plus Quasi-interpretations

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