On context semantics and interaction nets

Perrinel, Matthieu

doi:10.1145/2603088.2603155

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…In a previous work [25], we defined a context semantics for interaction nets: a wellbehaved class of graph rewriting systems [19] based on proof-nets. Interaction net is not a singe system, but a set of such systems.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Paths-based criteria and application to linear logic subsystems characterizing polynomial time

Perrinel

2018

Information and Computation

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Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial time (Ptime). In this paper we study the complexity of linear logic proof-nets and propose three semantic criteria based on context semantics: stratification, dependence control and nesting. Stratification alone entails an elementary time bound, the three criteria entail together a polynomial time bound.These criteria can be used to prove the complexity soundness of several existing variants of linear logic. We define a decidable syntactic subsystem of linear logic: S DNLL. We prove that the proof-nets of SDNLL satisfy the three criteria, which implies that S DNLL is sound for Ptime. Several previous subsystems of linear logic characterizing polynomial time (LLL, mL 4 , maximal system of MS ) are embedded in S DNLL, proving its Ptime completeness.

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Section: Conclusion and Further Workmentioning

confidence: 99%

Paths-based criteria and application to linear logic subsystems characterizing polynomial time

Perrinel

2018

Information and Computation

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“…Various formal definitions of interaction nets can be found elsewhere in the literature [Maz06;Vau07;Per14], but an intuitive understanding of the underlying graph-rewriting technology should be sufficient in the context of this paper.…”

Section: Interaction Nets and Their Parallel Reductionmentioning

confidence: 99%

The complexity of interaction

GimenezStéphane

MoserGeorg

2016

SIGPLAN Not.

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In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and scheduled types, we certify concrete time, space and space-time complexity bounds for both sequential and parallel reductions of interaction-net programs by suitably assigning complexity potentials to typed nodes. The relevance of this approach is illustrated on archetypal programming examples. The provided analysis is precise, compositional and is, in theory, not restricted to particular complexity classes.

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“…The reader is assumed to be familiar with interaction nets as described by Lafont in [18]. Various formal definitions of interaction nets can be found elsewhere in the literature [27,29,33], but an intuitive understanding of the underlying graph-rewriting technology should be sufficient in the context of this paper.…”

Section: Interaction Nets and Their Parallel Reductionmentioning

confidence: 99%

“…Complexity Analysis of Interaction Nets Despite the conceptual importance of interaction nets, little is known about complexity analysis of reductions in interaction nets, Perrinel's work [29] on context semantics of interaction nets [13] being the exception. Perrinel employs context semantics to assign a global weight W to a net N which bounds the length of sequential reductions.…”

Section: Related Workmentioning

confidence: 99%