We present a subsystem of second order Linear Logic with restricted rules for expo-nentials so that proofs correspond to polynomial time algorithms, and vice-versa.
We propose a new kind of programming language, with the following features: <list><item>a simple graph rewriting semantics, </item><item>a complete symmetry between constructors and destructors, </item><item>a type discipline for deterministic and deadlock-free (microscopic) parallelism. </item></list><italic>Interaction nets</italic> generalize Girard's… (More)
It is shown that a very simple system of interaction com-binators, with only 3 symbols and 6 rules, is a universal model of distributed computation, in a sense that will be made precise. This paper is the continuation of the au-thor's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is… (More)
The multiplicative fragment of second order propositional linear logic is shown to be undecidable.
To show that a formula A is not provable in propositional classical logic, it suuces to exhibit a nite boolean model which does not satisfy A. A similar property holds in the intuitionistic case, with Kripke models instead of boolean models (see for instance TvD88]). One says that the propositional classical logic and the propositional intuitionistic logic… (More)
Recently, Lincoln, Scedrov and Shankar showed that the multi-plicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicative-additive fragment, but it does not work in the classical case, because second order classical logic is decidable. Here… (More)