Linear Constraint Systems as High-level Nets

Linear constraint systems are simple deductive systems based on the main underlying idea of linear logic: hypotheses represent physical resources which are consumed by the entailment relation. For such systems, we define back-and-forth translations into a class of high-level Petri nets. Using the specific properties of that class of nets, and previous results about the complexity of the reachability problem for such nets, we examine the complexity of the entailment problem for finitely generated linear constraint systems and we show that it is NP-complete

Palamidessi: Linear constraint systems as high-level nets

Abstract. Linear constraint systems are simple deductive systems based on the main underlying idea of linear logic: hypotheses represent physical resources which are consumed by the entailment relation. For such systems, we define back-and-forth translations into a class of high-level Petri nets. Using the specific properties of that class of nets, and previous results about the complexity of the reachability problem for such nets, we examine the complexity of the entailment problem for finitely generated linear constraint systems and we show that it is NP-complete.