21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
Obsessional Cliques: A Semantic Characterization of Bounded Time Complexity
Seattle, Washington
August 12-August 15
ISBN: 0-7695-2631-4
We give a semantic characterization of bounded complexity proofs. We introduce the notion of obsessional clique in the relational model of linear logic and show that restricting the morphisms of the category REL to obsessional cliques yields models of ELL and SLL. Conversely, we prove that these models are relatively complete: an LL proof whose interpretation is an obsessional clique is always an ELL/SLL proof. These results are achieved by introducing a system of ELL/SLL untyped proof-nets, which is both correct and complete with respect to elementary/ polynomial time
Citation:
Olivier Laurent, Lorenzo Tortora de Falco, "Obsessional Cliques: A Semantic Characterization of Bounded Time Complexity," lics, pp.179-188, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), 2006