Аннотация:In this paper we consider two associative noncommutative analogs of Girard's linear logic. These are Abrusci's noncommutative linear logic and Yetter's cyclic linear logic.
We give a linear-length translation from the multiplicative fragment of Abrusci's noncommutative linear logic into the multiplicative fragment of Yetter's cyclic linear logic and vice versa. As a corollary we obtain that the decidability problems for derivability in these two calculi are in polynomial time reducible to each other.