A higher-order characterization of probabilistic polynomial time

Lago, Ugo Dal; Toldin, Paolo Parisen

doi:10.1016/j.ic.2014.10.009

Cited by 8 publications

(9 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…What is even more exciting, however, is the application of the ideas presented here to polynomial time computation. This would allow to go towards a characterization of expected polynomial time computation, thus greatly improving on the existing works on the implicit complexity of probabilistic systems [5,7], which only deals with worst-case execution time. The authors are currently engaged in that.…”

Section: Discussionmentioning

confidence: 99%

On Higher-Order Probabilistic Subrecursion

Breuvart¹,

Lago²,

Herrou³

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

International audienceWe study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like Gödel's T with various forms of probabilistic choice operators may result in calculi which are not equivalent as for the class of distributions they give rise to, although they all guarantee almost-sure termination. Along the way, we introduce a probabilistic variation of the classic reducibility technique, and we prove that the simplest form of probabilistic choice leaves the expressive power of T essentially unaltered. The paper ends with some observations about functional expressivity: expectedly, all the considered calculi represent precisely the functions which T itself represents

show abstract

Section: Discussionmentioning

confidence: 99%

On Higher-Order Probabilistic Subrecursion

Breuvart¹,

Lago²,

Herrou³

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section we introduce RSLR [4], a λ-calculus for probabilistic polynomial time computation, obtained by extending Hofmann's SLR [11] with an operator for binary probabilistic choice. Compared to other presentations of the same calculus, we consider a call-by-value reduction but elide nonlinear function spaces and pairs.…”

Section: Characterizing Probabilistic Polynomial Timementioning

confidence: 99%

“…Higher-order types clearly allow a certain degree of interaction, but probability and complexity are usually absent: reduction is deterministic (or at least confluent), while the expressive power of λ-calculi tends to be very high. This picture has somehow changed in the last ten years: there have been some successful attempts at giving probabilistic λ-calculi whose representable functions coincide with the ones which can be computed by PPT algorithms [14,17,4]. These calculi invariably took the form of restrictions on Gödel's T, endowed with a form of binary probabilistic choice.…”

Section: Introductionmentioning

confidence: 99%

“…All this has been facilitated by implicit computational complexity, which offers the right idioms to start from [10], themselves based on linearity and ramification. The emphasis in all these works were either the characterization of probabilistic complexity classes [4], or more often security [17,15,16]: one could see λ-calculi as a way to specify cryptographic constructions and adversaries for them. The crucial idea here is that computational indistinguishability can be formulated as a form of This work is partially supported by the ANR project 12IS02001 PACE.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we study notions of equivalence and distance in one of these λ-calculi, called RSLR [4]. More precisely:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Equivalences, Metrics, and Polynomial Time

Cappai

Lago²

2015

Fundamentals of Computation Theory

Self Cite

View full text Add to dashboard Cite

International audienceInteractive behaviors are ubiquitous in modern cryptography, but are also present in λ-calculi, in the form of higher-order constructions. Traditionally, however, typed λ-calculi simply do not fit well into cryptography , being both deterministic and too powerful as for the complexity of functions they can express. We study interaction in a λ-calculus for probabilistic polynomial time computable functions. In particular, we show how notions of context equivalence and context metric can both be characterized by way of traces when defined on linear contexts. We then give evidence on how this can be turned into a proof methodology for computational indistinguishability, a key notion in modern cryptography. We also hint at what happens if a more general notion of a context is used

show abstract

Algorithmically Broad Languages for Polynomial Time and Space

Leivant

2021

Logic, Language, Information, and Computation

View full text Add to dashboard Cite

A higher-order characterization of probabilistic polynomial time

Cited by 8 publications

References 6 publications

On Higher-Order Probabilistic Subrecursion

On Higher-Order Probabilistic Subrecursion

On Equivalences, Metrics, and Polynomial Time

Algorithmically Broad Languages for Polynomial Time and Space

Contact Info

Product

Resources

About