  Proof nets are a syntax for linear logic proofs which gives a coarser notion
of proof equivalence with respect to syntactic equality together with an
intuitive geometrical representation of proofs.
  In this paper we give an alternative $2$-dimensional syntax for
multiplicative linear logic derivations. The syntax of string diagrams
authorizes the definition of a framework where the sequentializability of a
term, i.e. deciding whether the term corresponds to a correct derivation, can
be verified in linear time.
  Furthermore, we can use this syntax to define a denotational semantics for
multiplicative linear logic with units by means of equivalence classes of proof
diagrams modulo a terminating rewriting.
