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Correctness of multiplicative proof nets is linear
 In LICS
, 1999
"... We reformulate Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasilinear algorithm. Linearity is obtained after observing that the disjointset unionfind at the core of the unification c ..."
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Cited by 34 (3 self)
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We reformulate Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasilinear algorithm. Linearity is obtained after observing that the disjointset unionfind at the core of the unification criterion is a special case of unionfind with a real linear time solution. 1
Proof nets, Garbage, and Computations
, 1997
"... We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty isin a complete set of rewriting rules for cutelimination in presence of weakening (which requires garbage collection). The proposed reduction s ..."
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Cited by 7 (6 self)
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We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty isin a complete set of rewriting rules for cutelimination in presence of weakening (which requires garbage collection). The proposed reduction system is strongly normalizing and confluent.
Retractile Proof Nets of the Purely Multiplicative and Additive Fragment of Linear Logic
"... Abstract. Proof nets are a parallel syntax for sequential proofs of linear logic, firstly introduced by Girard in 1987. Here we present and intrinsic (geometrical) characterization of proof nets, that is a correctness criterion (an algorithm) for checking those proof structures which correspond to p ..."
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Cited by 3 (1 self)
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Abstract. Proof nets are a parallel syntax for sequential proofs of linear logic, firstly introduced by Girard in 1987. Here we present and intrinsic (geometrical) characterization of proof nets, that is a correctness criterion (an algorithm) for checking those proof structures which correspond to proofs of the purely multiplicative and additive fragment of linear logic. This criterion is formulated in terms of simple graph rewriting rules and it extends an initial idea of a retraction correctness criterion for proof nets of the purely multiplicative fragment of linear logic presented by Danos in his Thesis in 1990. 1
Correctness of multiplicative (and exponential) proof structures is l complete
 Lecture Notes in Computer Science
, 2007
"... Abstract. We provide a new correctness criterion for unitfree MLL proof structures and MELL proof structures with units. We prove that deciding the correctness of a MLL and of a MELL proof structure is NLcomplete. We also prove that deciding the correctness of an intuitionistic multiplicative ess ..."
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Cited by 3 (1 self)
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Abstract. We provide a new correctness criterion for unitfree MLL proof structures and MELL proof structures with units. We prove that deciding the correctness of a MLL and of a MELL proof structure is NLcomplete. We also prove that deciding the correctness of an intuitionistic multiplicative essential net is NLcomplete.
A linear algorithm for mll proof net correctness and sequentialization. Theoretical Computer Science 412(20
, 2011
"... The paper presents in full details the first linear algorithm given in the literature [6] implementing proof structure correctness for multiplicative linear logic without units. The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification. As ..."
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Cited by 3 (0 self)
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The paper presents in full details the first linear algorithm given in the literature [6] implementing proof structure correctness for multiplicative linear logic without units. The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasilinear algorithm. Linearity is obtained after observing that the disjointset unionfind at the core of the unification criterion is a special case of unionfind with a real linear time solution. 1
Correctness of Linear Logic Proof Structures is NLComplete (rapport interne LIPN Decembre 2008)
, 2009
"... We provide new correctness criteria for all fragments (multiplicative, exponential, additive) of linear logic. We use these criteria for proving that deciding the correctness of a linear logic proof structure is NLcomplete. ..."
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Cited by 1 (0 self)
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We provide new correctness criteria for all fragments (multiplicative, exponential, additive) of linear logic. We use these criteria for proving that deciding the correctness of a linear logic proof structure is NLcomplete.
Introduction to linear logic and ludics, Part I
, 2004
"... This twoparts paper offers a survey of linear logic and ludics, which were introduced by Girard ..."
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This twoparts paper offers a survey of linear logic and ludics, which were introduced by Girard