Some trade-off results for polynomial calculus
2013 (English)In: STOC '13 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, Association for Computing Machinery (ACM), 2013, 813-822 p.Conference paper (Refereed)
We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true size-space trade-offs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by extending essentially all known size-space trade-offs for resolution to PC and PCR. As such, our results cover space complexity from constant all the way up to exponential and yield mostly superpolynomial or even exponential size blow-ups. Since the upper bounds in our trade-offs hold for resolution, our work shows that there are formulas for which adding algebraic reasoning on top of resolution does not improve the trade-off properties in any significant way. As byproducts of our analysis, we also obtain trade-offs between space and degree in PC and PCR exactly matching analogous results for space versus width in resolution, and strengthen the resolution trade-offs in [Beame, Beck, and Impagliazzo '12] to apply also to k-CNF formulas.
Place, publisher, year, edition, pages
Association for Computing Machinery (ACM), 2013. 813-822 p.
, Proceedings of the Annual ACM Symposium on Theory of Computing, ISSN 0737-8017
Degree, PCR, Pebble games, Pebbling formulas, Polynomial calculus, Proof complexity, Resolution, Size, Space, Trade-offs, Tseitin formulas
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-134132DOI: 10.1145/2488608.2488711ScopusID: 2-s2.0-84879820217ISBN: 978-145032029-0OAI: oai:DiVA.org:kth-134132DiVA: diva2:665184
45th Annual ACM Symposium on Theory of Computing, STOC 2013; Palo Alto, CA; United States; 1 June 2013 through 4 June 2013
QC 201311192013-11-192013-11-182013-11-19Bibliographically approved