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Soft lambdacalculus: a language for polynomial time computation
 In Proc. FoSSaCS, Springer LNCS 2987
, 2004
"... Abstract. Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambdacalculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time. ..."
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Cited by 19 (2 self)
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Abstract. Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambdacalculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time. We then extend the type system of Soft logic with recursive types. This allows us to consider nonstandard types for representing lists. Using these datatypes we examine the concrete expressiveness of Soft lambdacalculus with the example of the insertion sort algorithm. 1
Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity
 LOGIC JOURNAL OF THE IGPL
, 2003
"... Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessi ..."
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Cited by 7 (5 self)
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Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural twosorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result
A soft type assignment system for λcalculus
 In Proceedings of the Computer Science Logic, 21st International Workshop  CSL’07
"... Abstract. Soft Linear Logic (SLL) is a subsystem of secondorder linear logic with restricted rules for exponentials, which is correct and complete for PTIME. We design a type assignment system for the λcalculus (STA), which assigns to λterms as types (a proper subset of) SLL formulas, in such a w ..."
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Cited by 5 (2 self)
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Abstract. Soft Linear Logic (SLL) is a subsystem of secondorder linear logic with restricted rules for exponentials, which is correct and complete for PTIME. We design a type assignment system for the λcalculus (STA), which assigns to λterms as types (a proper subset of) SLL formulas, in such a way that typable terms inherit the good complexity properties of the logical system. Namely STA enjoys subject reduction and normalization, and it is correct and complete for PTIME and FPTIME.
Uniform circuits, � Boolean proof nets
"... Abstract. The relationship between Boolean proof nets of multiplicative linear logic (APN) and Boolean circuits has been studied [Ter04] in a nonuniform setting. We refine the results taking care of uniformity: the relationship can be expressed in term of the (Turing) polynomial hierarchy. We give ..."
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Cited by 2 (2 self)
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Abstract. The relationship between Boolean proof nets of multiplicative linear logic (APN) and Boolean circuits has been studied [Ter04] in a nonuniform setting. We refine the results taking care of uniformity: the relationship can be expressed in term of the (Turing) polynomial hierarchy. We give a proofsasprograms correspondence between proof nets and deterministic as well as nondeterministic Boolean circuits with a uniform depthpreserving simulation of each other. The Boolean proof nets class m�BN(poly) is built on multiplicative and additive linear logic with a polynomial amount of additive connectives as the nondeterministic circuit class NNC(poly) is with nondeterministic variables. We obtain uniformAPN = NC and m�BN(poly) = NNC(poly) = NP. 1
Proofs as executions
, 2012
"... Abstract. This paper proposes a new interpretation of the logical contents of programs in the context of concurrent interaction, wherein proofs correspond to valid executions of a processes. A type system based on linear logic is used, in which a given process has many different types, each typing c ..."
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Cited by 1 (0 self)
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Abstract. This paper proposes a new interpretation of the logical contents of programs in the context of concurrent interaction, wherein proofs correspond to valid executions of a processes. A type system based on linear logic is used, in which a given process has many different types, each typing corresponding to a particular way of interacting with its environment and cut elimination corresponds to executing the process in a given interaction scenario. A completeness result is established, stating that every lockavoiding execution of a process in some environment corresponds to a particular typing. Besides traces, types contain precise information about the flow of control between a process and its environment, and proofs are interpreted as composable schedulings of processes. In this interpretation, logic appears as a way of making explicit the flow of causality between interacting processes. 1
Linear Logic by Levels and Bounded Time Complexity
, 2009
"... This work deals with the characterization of elementary and deterministic polynomial time computation in linear logic through the proofsasprograms correspondence. Girard’s seminal results, concerning elementary and light linear logic, use a principle called stratification to ensure the complexity b ..."
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This work deals with the characterization of elementary and deterministic polynomial time computation in linear logic through the proofsasprograms correspondence. Girard’s seminal results, concerning elementary and light linear logic, use a principle called stratification to ensure the complexity bound on the cutelimination procedure. Here, we propose a more flexible control principle, that of indexing, which allows us to extend Girard’s systems while keeping the same complexity properties. A consequence of the higher flexibility of indexing with respect to stratification is the absence of boxes for handling the § modality. We finally propose a variant of our polytime system in which the § modality is only allowed on atoms, and which may thus serve as a basis for developing λcalculus type assignment systems with more efficient typing algorithms than existing ones.