Stratified Bounded Affine Logic for Logarithmic Space

Ulrich Schopp
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
A number of complexity classes, most notably PTIME, have been characterised by sub-systems of linear logic. In this paper we show that the functions computable in logarithmic space can also be characterised by a restricted version of linear logic. We introduce Stratified Bounded Affine Logic (SBAL), a restricted version of Bounded Linear Logic, in which not only the modality ! but also the universal quantifier is bounded by a resource polynomial. We show that the proofs of certain sequents in
more » ... AL represent exactly the functions computable logarithmic space. The proof that SBAL-proofs can be compiled to LOGSPACE functions rests on modelling computation by interaction dialogues in the style of game semantics. We formulate the compilation of SBAL-proofs to space-efficient programs as an interpretation in a realisability model, in which realisers are taken from a Geometry of Interaction situation.
doi:10.1109/lics.2007.45 dblp:conf/lics/Schopp07 fatcat:rblt4b5qsrgy3kaqtftonbex5u