Quasi-interpretations a way to control resources

Bonfante, Guillaume; Marion, Jean-Yves; Moyen, Jean-Yves

doi:10.1016/j.tcs.2011.02.007

Cited by 50 publications

(92 citation statements)

References 21 publications

(43 reference statements)

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“…Using this definition and the previous bijection among N 4 and N we can see a transition of a CT M as a function from N to N. We omit its definition and, by a slight abuse of notation, we denote such a function still by N . Furthermore, in a way analogous to the previous cases, it is possible to show that such a function is partial recursive.…”

Section: Equivalence Resultsmentioning

confidence: 99%

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Probabilistic Recursion Theory and Implicit Computational Complexity

Lago

Zuppiroli

2014

Theoretical Aspects of Computing – ICTAC 2014

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In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability . We then prove the equiexpressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursiontheoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.iii iv

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Section: Equivalence Resultsmentioning

confidence: 99%

“…This issue has been pointed out by several authors as i.e. Hofmann [18], and advances have been made in the direction of more liberal ICC systems: some examples are type systems for non-size-increasing computation (Hofmann [18]) and quasi-interpretations (Bonfante et al [4]). …”

Section: Chapter 3 Implicit Computational Complexitymentioning

confidence: 99%

Probabilistic Recursion Theory and Implicit Computational Complexity

Lago

Zuppiroli

2014

Theoretical Aspects of Computing – ICTAC 2014

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“…Our approach is related to size analysis with polynomial quasi-interpretations [2,4]. There, a program is interpreted as a monotonic polynomial extended with the max operation.…”

Section: Related Workmentioning

confidence: 99%

Collected Size Semantics for Strict Functional Programs over General Polymorphic Lists

Shkaravska

Eekelen

Tamalet³

2014

Foundational and Practical Aspects of Resource Analysis

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Abstract. Size analysis can be an important part of heap consumption analysis. This paper is a part of ongoing work about typing support for checking output-on-input size dependencies for function definitions in a strict functional language. A significant restriction for our earlier results is that inner data structures (e.g. in a list of lists) all must have the same size. Here, we make a big step forwards by overcoming this limitation via the introduction of higher-order size annotations such that variate sizes of inner data structures can be expressed. In this way the analysis becomes applicable for general, polymorphic nested lists.

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“…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: 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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Quasi-interpretations a way to control resources

Cited by 50 publications

References 21 publications

Probabilistic Recursion Theory and Implicit Computational Complexity

Probabilistic Recursion Theory and Implicit Computational Complexity

Collected Size Semantics for Strict Functional Programs over General Polymorphic Lists

Characterizing polynomial time complexity of stream programs using interpretations

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