  This paper presents proof nets for multiplicative-additive linear logic
(MALL), called conflict nets. They are efficient, since both correctness and
translation from a proof are p-time (polynomial time), and abstract, since they
are invariant under transposing adjacent &-rules.
  A conflict net on a sequent is concise: axiom links with a conflict relation.
Conflict nets are a variant of (and were inspired by) combinatorial proofs
introduced recently for classical logic: each can be viewed as a maximal map
(homomorphism) of contractible coherence spaces (P_4-free graphs, or cographs),
from axioms to sequent.
  The paper presents new results for other proof nets: (1) correctness and cut
elimination for slice nets (Hughes / van Glabbeek 2003) are p-time, and (2) the
cut elimination proposed for monomial nets (Girard 1996) does not work. The
subtleties which break monomial net cut elimination also apply to conflict
nets: as with monomial nets, existence of a confluent cut elimination remains
an open question.
