A P-Time Completeness Proof for Light Logics

Roversi, Luca

doi:10.1007/3-540-48168-0_33

Cited by 25 publications

(19 citation statements)

References 4 publications

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“…In particular, some reader may have noticed that the configurations of the machines are not encoded obviously, like in Girard [1998], as recalled in Figure 59. Roversi [1999] discusses about why such an encoding can not work. Roughly, it does not allow to write an iterable function config2config, which is basic to produce the whole encoding.…”

Section: Discussionmentioning

confidence: 98%

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Intuitionistic Light Affine Logic

Asperti

Roversi

2002

ACM Trans. Comput. Logic

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130

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This article is a structured introduction to Intuitionistic Light Affine Logic (ILAL). ILAL has a polynomially costing normalization, and it is expressive enough to encode, and simulate, all PolyTime Turing machines. The bound on the normalization cost is proved by introducing the proof-nets for ILAL. The bound follows from a suitable normalization strategy that exploits structural properties of the proof-nets. This allows us to have a good understanding of the meaning of the § modality, which is a peculiarity of light logics. The expressive power of ILAL is demonstrated in full detail. Such a proof gives a hint of the nontrivial task of programming with resource limitations, using ILAL derivations as programs.

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Section: Discussionmentioning

confidence: 98%

“…In Asperti [1998], Light Affine Logic (LAL), a slight variation of LLL, was introduced. Roversi [1999] made some basic observations about how to build a proof of the representation power of LAL, and, indirectly, of LLL as well. This article is a monolithic reworking of both papers with the hope to make the subject more widely accessible.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Light Affine Logic

Asperti

Roversi

2002

ACM Trans. Comput. Logic

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130

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“…With second-order quantifiers there is also a completeness result (see [2,22]). It is important to note that the statement of Proposition 4 refers to the number of normalization steps of proof-nets and not to the -reduction of the lambda-term (t u) itself.…”

Section: Remarkmentioning

confidence: 95%

Type inference for light affine logic via constraints on words

Baillot

2004

Theoretical Computer Science

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Light Affine Logic (LAL) is a system due to Girard and Asperti capturing the complexity class P in a proof-theoretical approach based on Linear Logic. LAL provides a typing for lambda-calculus which guarantees that a well-typed program is executable in polynomial time on any input. We prove that the LAL type inference problem for lambda-calculus is decidable (for propositional LAL). To establish this result we reformulate the type-assignment system into an equivalent one which makes use of subtyping and is more flexible. We then use a reduction to a satisfiability problem for a system of inequations on words over a binary alphabet, for which we provide a decision procedure.

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“…It has two parameters L and B and builds on the core mechanism of the predecessor for Church numerals [14,12] inside typing systems like TFA. For any types A, α, let…”

Section: Meta-combinatorsmentioning

confidence: 99%

Light combinators for finite fields arithmetic

Canavese

Cesena²,

Ouchary

et al. 2015

Science of Computer Programming

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We supply a library of pure functional terms with the following features: (i) any term can be typed in a type system which implicitly certifies it belongs to the class of terms which evaluate in polynomial time; (ii) they implement all the basic functions required to perform arithmetic on binary finite fields.The type assignment system is Type Functional Assembly (TFA), an extension of Dual Light Affine Logic (DLAL). The development of the whole library shows we can think of TFA as a domain specific language in which the composition of variants of standard functional programming schemes drives a programmer to think of implementations under non standard patterns.

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A P-Time Completeness Proof for Light Logics

Abstract: Abstract. We explain why the original proofs of P-Time completeness for Light Affine Logic and Light Linear Logic can not work, and we fully develop a working one.

Cited by 25 publications

References 4 publications

Intuitionistic Light Affine Logic

Intuitionistic Light Affine Logic

Type inference for light affine logic via constraints on words

Light combinators for finite fields arithmetic

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