Lambda calculus characterizations of poly-time

Leivant, Daniel; Marion, Jean-Yves

doi:10.1007/bfb0037112

Cited by 69 publications

(66 citation statements)

References 17 publications

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“…The recent works of Bellantoni and Cook [BC92] and of Leivant [Lei95,LM93] suggests another direction by mean of data tiering which is called implicit computational complexity. There are no more explicit resource bounds.…”

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

Self Cite

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“…These latter characterizations are inspired by former characterizations of type-1 polynomial time complexity based on ramification [8,9]. This line of research has led to new developments of other ICC tools and in particular to the use of (polynomial) interpretations in order to characterize the classes of functions computable in polynomial time or space [10,11].…”

Section: Introductionmentioning

confidence: 97%

Characterizing polynomial time complexity of stream programs using interpretations

Férée

Hainry

Hoyrup

et al. 2015

Theoretical Computer Science

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This paper provides a criterion based on interpretation methods on term rewrite systems in order to characterize the polynomial time complexity of second order functionals. For that purpose it introduces a first order functional stream language that allows the programmer to implement second order functionals. This characterization is extended through the use of exp-poly interpretations as an attempt to capture the class of Basic Feasible Functionals (bff). Moreover, these results are adapted to provide a new characterization of polynomial time complexity in computable analysis. These characterizations give a new insight on the relations between the complexity of functional stream programs and the classes of functions computed by Oracle Turing Machine, where oracles are treated as inputs.

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“…Leivant and Marion [18] give a λ-calculus characterization of Ptime. The main novelty is the use of the concept of "tiers" in the sense of different representations of data: as words (i.e.…”

Section: Introductionmentioning

confidence: 99%