- Full text PDF available (22)
- This year (0)
- Last 5 years (1)
- Last 10 years (8)
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)
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.
Boolean circuits are used to represent programs on finite data. Reversible Boolean circuits and quantum Boolean circuits have been introduced to modelize some physical aspects of computation. Those notions are essential in complexity theory, but we claim that a deep mathematical theory is needed to make progress in this area. For that purpose, the recent… (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)
Girard’s linear logic is a promising tool for understanding phenomena of interaction and concurrency in computing. This logic is “classical” in the sense that hypotheses can be considered as (negated) conclusions, and vice versa. So it is not possible to interpret formulae as sets and proofs as functions, as in the intuitionistic case. Here, we propose a… (More)
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)
The multiplicative fragment of second order propositional linear logic is shown to be undecidable.