Author

# Paolo Tranquilli

Other affiliations: University of Lyon

Bio: Paolo Tranquilli is an academic researcher from Paris Diderot University. The author has contributed to research in topics: Proof complexity & Calculus of communicating systems. The author has an hindex of 4, co-authored 4 publications receiving 50 citations. Previous affiliations of Paolo Tranquilli include University of Lyon.

##### Papers

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03 Dec 2009TL;DR: This work defines parallel reduction in resource calculus and applies the technique by Tait and Martin-Lof to achieve confluence, and slightly generalizes a technique by Takahashi to obtain a standardization result.

Abstract: We study the resource calculus --- the non-lazy version of Boudol's *** -calculus with resources. In such a calculus arguments may be finitely available and mixed, giving rise to nondeterminism, modelled by a formal sum. We define parallel reduction in resource calculus and we apply, in such a nondeterministic setting, the technique by Tait and Martin-Lof to achieve confluence. Then, slightly generalizing a technique by Takahashi, we obtain a standardization result.

33 citations

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07 Sep 2009TL;DR: It is proved that pure differential nets are Church-Rosser modulo such equivalences, which generalizes to linear logic regular proof nets, and uses a result of finiteness of developments, given by strong normalization when blocking a suitable notion of "new" cuts.

Abstract: We study the confluence of Ehrhard and Regnier's differential nets with exponential promotion, in a pure setting. Confluence fails with promotion and codereliction in absence of associativity of (co)contractions. We thus introduce it as a necessary equivalence, together with other optional ones. We then prove that pure differential nets are Church-Rosser modulo such equivalences. This result generalizes to linear logic regular proof nets, where the same notion of equivalence was already studied in the literature, but only with respect to the problem of normalization in a typed setting. Our proof uses a result of finiteness of developments, which in this setting is given by strong normalization when blocking a suitable notion of "new" cuts.

9 citations

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TL;DR: The conservation theorem for differential nets – the graph-theoretical syntax of the differential extension of Linear Logic (Ehrhard and Regnier's DiLL) is proved, which turns the quest for strong normalisation into one for non-erasing weak normalisation (WN), and indeed this result is used to prove SN of simply typed DiLL.

Abstract: We prove the conservation theorem for differential nets – the graph-theoretical syntax of the differential extension of Linear Logic (Ehrhard and Regnier's DiLL). The conservation theorem states that the property of having infinite reductions (here infinite chains of cut elimination steps) is preserved by non-erasing steps. This turns the quest for strong normalisation (SN) into one for non-erasing weak normalisation (WN), and indeed we use this result to prove SN of simply typed DiLL (with promotion). Along the way to the theorem we achieve a number of additional results having their own interest, such as a standardisation theorem and a slightly modified system of nets, DiLL ∂ϱ.

6 citations

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16 Sep 2008

TL;DR: This work gives the first proof of semantical soundness of hypercoherent spaces with respect to proof nets entirely based on graph theoretical trips, in the style of Girard's proof ofSemantical Soundness of coherent spaces for proof nets of the multiplicative fragment of linear logic.

Abstract: We give a graph theoretical criterion on multiplicative additive linear logic (MALL) cut-free proof structures that exactly characterizes those whose interpretation is a hyperclique in Ehrhard's hypercoherent spaces. This criterion is strictly weaker than the one given by Hughes and van Glabbeek characterizing proof nets (i.e. desequentialized sequent calculus proofs). We thus also give the first proof of semantical soundness of hypercoherent spaces with respect to proof nets entirely based on graph theoretical trips, in the style of Girard's proof of semantical soundness of coherent spaces for proof nets of the multiplicative fragment of linear logic.

5 citations

##### Cited by

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01 Jan 2002

TL;DR: This chapter presents the basic concepts of term rewriting that are needed in this book and suggests several survey articles that can be consulted.

Abstract: In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

501 citations

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TL;DR: By understanding the GPU architecture and its massive parallelism programming model, one can overcome many of the technical limitations found along the way, design better GPU-based algorithms for computational physics problems and achieve speedups that can reach up to two orders of magnitude when compared to sequential implementations.

Abstract: Parallel computing has become an important subject in the field of computer science and has proven to be critical when researching high performance solutions. The evolution of computer architectures ( multi-core and many-core ) towards a higher number of cores can only confirm that parallelism is the method of choice for speeding up an algorithm. In the last decade, the graphics processing unit, or GPU, has gained an important place in the field of high performance computing (HPC) because of its low cost and massive parallel processing power. Super-computing has become, for the first time, available to anyone at the price of a desktop computer. In this paper, we survey the concept of parallel computing and especially GPU computing. Achieving efficient parallel algorithms for the GPU is not a trivial task, there are several technical restrictions that must be satisfied in order to achieve the expected performance. Some of these limitations are consequences of the underlying architecture of the GPU and the theoretical models behind it. Our goal is to present a set of theoretical and technical concepts that are often required to understand the GPU and its massive parallelism model. In particular, we show how this new technology can help the field of computational physics, especially when the problem is data-parallel. We present four examples of computational physics problems; n-body, collision detection, Potts model and cellular automata simulations. These examples well represent the kind of problems that are suitable for GPU computing. By understanding the GPU architecture and its massive parallelism programming model, one can overcome many of the technical limitations found along the way, design better GPU-based algorithms for computational physics problems and achieve speedups that can reach up to two orders of magnitude when compared to sequential implementations.

158 citations

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TL;DR: Differential linear logic as mentioned in this paper enriches linear logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction, and introduces a simple categorical condition on these models under which a general antiderivative operation becomes available.

Abstract: Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic and a categorical axiomatization of its denotational models. We also introduce a simple categorical condition on these models under which a general antiderivative operation becomes available. Last we briefly describe the model of sets and relations and give a more detailed account of the model of finiteness spaces and linear and continuous functions.

65 citations

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TL;DR: The notion of differential @l-category as an extension of Blute-Cockett-Seely's differential Cartesian categories is introduced and it is proved that differential@l-categories can be used to model the simply typed versions of the differential @ l-calculus and the resource calculus.

48 citations

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20 Mar 2010TL;DR: This work defines a term solvable whenever there is a simple head context reducing the term into a sum where at least one addend is the identity, and gives a syntactical, operational and logical characterization of this kind of solvability.

Abstract: The resource calculus is an extension of the λ-calculus allowing to model resource consumption. Namely, the argument of a function comes as a finite multiset of resources, which in turn can be either linear or reusable, giving rise to non-deterministic choices, expressed by a formal sum. Using the λ-calculus terminology, we call solvable a term that can interact with the environment: solvable terms represent meaningful programs. Because of the non-determinism, different definitions of solvability are possible in the resource calculus. Here we study the optimistic (angelical, or may) notion, and so we define a term solvable whenever there is a simple head context reducing the term into a sum where at least one addend is the identity. We give a syntactical, operational and logical characterization of this kind of solvability.

43 citations