Title: Simulating Linear Logic in 1-Only Linear Logic,
Abstract: Linear Logic was introduced by Girard as a resource-sensitive refinement of
classical logic. It turned out that full propositional Linear Logic is
undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more
expressive than (modalized) classical or intuitionistic logic. In this paper we
focus on the study of the simplest fragments of Linear Logic, such as the
one-literal and constant-only fragments (the latter contains no literals at
all). Here we demonstrate that all these extremely simple fragments of Linear
Logic (one-literal, $\bot$-only, and even unit-only) are exactly of the same
expressive power as the corresponding full versions. We present also a complete
computational interpretation (in terms of acyclic programs with stack) for
bottom-free Intuitionistic Linear Logic. Based on this interpretation, we prove
the fairness of our encodings and establish the foregoing complexity results.