We study the problem of local and asynchronous computation in the context o
f multiplicative exponential linear logic (MELL) proof nets. The main novel
ty is in a complete set of rewriting rules for cut-elimination in presence
of weakening (which requires garbage collection). The proposed reduction sy
stem is strongly normalizing and confluent. The proofs are all based on pur
e syntactical reasonings. (C) 2001 Elsevier Science B,V. All rights reserve
d.