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14
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
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Cited by 111 (19 self)
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
From ProofNets to Interaction Nets
 Advances in Linear Logic
, 1994
"... Introduction If we consider the interpretation of proofs as programs, say in intuitionistic logic, the question of equality between proofs becomes crucial: The syntax introduces meaningless distinctions whereas the (denotational) semantics makes excessive identifications. This question does not hav ..."
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Cited by 73 (1 self)
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Introduction If we consider the interpretation of proofs as programs, say in intuitionistic logic, the question of equality between proofs becomes crucial: The syntax introduces meaningless distinctions whereas the (denotational) semantics makes excessive identifications. This question does not have a simple answer in general, but it leads to the notion of proofnet, which is one of the main novelties of linear logic. This has been already explained in [Gir87] and [GLT89]. The notion of interaction net introduced in [Laf90] comes from an attempt to implement the reduction of these proofnets. It happens to be a simple model of parallel computation, and so it can be presented independently of linear logic, as in [Laf94]. However, we think that it is also useful to relate the exact origin of interaction nets, especially for readers with some knowledge in linear logic. We take this opportunity to give a survey of the theory of proofnets, including a new proof of the sequentializ
A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 56 (10 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Interaction Combinators
 Information and Computation
, 1995
"... This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction ..."
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Cited by 47 (3 self)
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This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction
NREVERSAL of Fortune  The Thermodynamics of Garbage Collection
 In ACM Sigplan Notices
, 1977
"... The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to anal ..."
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Cited by 16 (0 self)
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The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to analyze a reversed computation arises in the context of static analysisliveness analysis, strictness analysis, type inference, etc. Traditional means for restoring a computation to a previous state involve checkpoints; checkpoints require time to copy, as well as space to store, the copied material. Traditional reverse abstract interpretation produces relatively poor information due to its inability to guess the previous values of assignedto variables. We propose an abstract computer model and a programming languageYLispwhose primitive operations are injective and hence reversible, thus allowing arbitrary undoing without the overheads of checkpointing. Such a computer can be built from reversible conservative logic circuits, with the serendipitous advantage of dissipating far less heat than traditional Boolean AND/OR/NOT circuits. Unlike functional languages, which have one &quot;state &quot; for all times, YLisp has at all times one &quot;state&quot;, with unique predecessor and successor states. Compiling into a reversible pseudocode can have benefits even when targeting a traditional computer. Certain optimizations, e.g., updateinplace, and compiletime garbage collection may be more easily performed, because the
A Calculus for Interaction Nets
, 1999
"... . Interaction nets are graphical rewriting systems which can be used as either a highlevel programming paradigm or a lowlevel implementation language. However, an operational semantics together with notions of strategy and normal form which are essential to reason about implementations, are not ea ..."
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Cited by 15 (8 self)
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. Interaction nets are graphical rewriting systems which can be used as either a highlevel programming paradigm or a lowlevel implementation language. However, an operational semantics together with notions of strategy and normal form which are essential to reason about implementations, are not easy to formalize in this graphical framework. The purpose of this paper is to study a textual calculus for interaction nets, with a formal operational semantics, which provides a foundation for implementation. In addition, we are able to specify in this calculus various strategies, and a type system which formalizes the notion of partition used to define semisimple nets. The resulting system can be seen as a kernel for a programming language, analogous to the calculus. 1 Introduction Interaction nets, introduced by Lafont [12], offer a graphical paradigm of computation based on net rewriting. They have proven themselves successful for application in computer science, most notably with the ...
The Algebraic Theory of Interaction Nets
, 1995
"... : The theory of interaction nets, invented by Lafont, is reexamined from the algebraic hypergraph rewriting perspective. Supersimple nets are defined and discussed, and some related classes of nets, the polysimple and monosimple classes, are defined and investigated. Their static properties are est ..."
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Cited by 9 (3 self)
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: The theory of interaction nets, invented by Lafont, is reexamined from the algebraic hypergraph rewriting perspective. Supersimple nets are defined and discussed, and some related classes of nets, the polysimple and monosimple classes, are defined and investigated. Their static properties are established, and the invariants that need to be preserved by rewriting are investigated in detail. It is shown that in the general case, contextspecific information may be used to ensure that rules actually preserve the characteristics of the rewritten net. Subordinate agents, which like logical constants for falsity may be introduced only in nonvoid contexts, are presented, and the ramifications of the theory in their presence are investigated, relating it to the simple and semisimple classes of Lafont. Under suitable conditions, describable in purely combinatorial terms, net rewriting systems possess ChurchRosser and Strong Normalisation properties usually associated with rewriting systems...
The Paradigm of Interaction (short Version)
, 1991
"... We present a unified framework subsuming wellknown models of sequential or parallel computation, such as Turing machines and cellular automata. We propose a notion of natural encoding motivated by issues in implementation and partial evaluation. The most remarkable feature is the GirardDanosR&apo ..."
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Cited by 1 (0 self)
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We present a unified framework subsuming wellknown models of sequential or parallel computation, such as Turing machines and cellular automata. We propose a notion of natural encoding motivated by issues in implementation and partial evaluation. The most remarkable feature is the GirardDanosR'egnier criterion for deadlockfree computation. This theory is a byproduct of linear logic.
Linear Naming: Experimental Software for Optimizing Communication Protocols
, 1998
"... We propose to design and implement significant new forms of procedure calling protocols, together with relevant supporting formal tools and implementation technology, and experiments that evaluate their feasibility and effectiveness. ..."
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We propose to design and implement significant new forms of procedure calling protocols, together with relevant supporting formal tools and implementation technology, and experiments that evaluate their feasibility and effectiveness.