Feasible Functions over Co-inductive Data

Ramyaa, Ramyaa; Leivant, Daniel

doi:10.1007/978-3-642-13824-9_16

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…The Implicit Computational Complexity (ICC) community has proposed characterizations of otm complexity classes using function algebra [3,4] and type systems [5,6] or recently as a logic [7].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Characterizing polynomial time complexity of stream programs using interpretations

Férée

Hainry

Hoyrup

et al. 2015

Theoretical Computer Science

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“…Pola also has a well-developed categorical semantics that, at present, RS 1 notably lacks. Ramyaa and Leivant [17,18] explore feasible first-order stream programming formalisms. In [17], they use infinite binary trees with string-labels to give a partial proof-theoretic characterization of the type-2 basic feasible functionals (BFF 2 ) of Mehlhorn [16] and Cook and Urquhart [7].…”

Section: Introductionmentioning

confidence: 99%

“…Ramyaa and Leivant [17,18] explore feasible first-order stream programming formalisms. In [17], they use infinite binary trees with string-labels to give a partial proof-theoretic characterization of the type-2 basic feasible functionals (BFF 2 ) of Mehlhorn [16] and Cook and Urquhart [7]. In [18], they give a definition of logspace stream computation and a schema of ramified co-recurrence which parallels Leivant's ramified recurrence of [14], and characterize logspace streams as those definable using 2-tier co-recurrences.…”

Section: Introductionmentioning

confidence: 99%

Ramified Structural Recursion and Corecursion

Danner¹,

Royer²

2012

Preprint

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We investigate feasible computation over a fairly general notion of data and codata. Specifically, we present a direct Bellantoni-Cookstyle normal/safe typed programming formalism, RS1 , that expresses feasible structural recursions and corecursions over data and codata specified by polynomial functors. (Lists, streams, finite trees, infinite trees, etc. are all directly definable.) A novel aspect of RS1 is that it embraces structure-sharing as in standard functional-programming implementations. As our data representations use sharing, our implementation of structural recursions are memoized to avoid the possibly exponentiallymany repeated subcomputations a naïve implementation might perform. We introduce notions of size for representations of data (accounting for sharing) and codata (using ideas from type-2 computational complexity) and establish that type-level 1 RS1 -functions have polynomial-bounded runtimes and satisfy a polynomial-time completeness condition. Also, restricting RS1 terms to particular types produces characterizations of some standard complexity classes (e.g., ω-regular languages, linear-space functions) and some less-standard classes (e.g., log-space streams).

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“…There are many works in the literature that study computability and (polynomial time) complexity of such functions [5,14]. The implicit computational complexity (ICC) community has proposed characterizations of such complexity classes using function algebra and types [9,16,8] or recently as a logic [15] . These results are reminiscent of former characterizations of type 1 polynomial time functions [4,2,12] that led to other ICC works using polynomial interpretations.…”

Section: Introductionmentioning

confidence: 99%

Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

Férée

Hainry

Hoyrup

et al. 2010

Algorithms and Computation

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Abstract. We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These characterizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over the reals, a particular case of type 2 functions, and we provide a characterization of polynomial time complexity in Recursive Analysis.

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Feasible Functions over Co-inductive Data

Cited by 4 publications

References 20 publications

Characterizing polynomial time complexity of stream programs using interpretations

Characterizing polynomial time complexity of stream programs using interpretations

Ramified Structural Recursion and Corecursion

Interpretation of Stream Programs: Characterizing Type 2 Polynomial Time Complexity

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