We present a functional characterization of deterministic logspace-computable predicates based on a variant (although not a subsystem) of propositional linear logic, which we call parsimonious logic. The resulting calculus is simply-typed and contains no primitive besides those provided by the underlying logical system, which makes it one of the simplest higher-order languages capturing logspace currently known. Completeness of the calculus uses the descriptive complexity characterization of logspace (we encode first-order logic with deterministic closure), whereas soundness is established by executing terms on a token machine (using the geometry of interaction).
@InProceedings{mazza:LIPIcs.CSL.2015.24, author = {Mazza, Damiano}, title = {{Simple Parsimonious Types and Logarithmic Space}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {24--40}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-90-3}, ISSN = {1868-8969}, year = {2015}, volume = {41}, editor = {Kreutzer, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.24}, URN = {urn:nbn:de:0030-drops-54053}, doi = {10.4230/LIPIcs.CSL.2015.24}, annote = {Keywords: implicit computational complexity, linear logic, geometry of interaction} }
Feedback for Dagstuhl Publishing