English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper gives nearly optimal lower bounds on the minimum degree of polynomial calculus refutations of Tseitin’s graph tautologies and the mod p counting principles, p ≥ 2. The lower bounds apply to the polynomial calculus over fields or rings. These are the first linear lower bounds for the polynomial calculus for k-CNF formulas. As a consequence, it follows that the Grobner basis algorithm, used as a heuristic for k-SAT, requires exponential time in the worst-case. Moreover, our lower bounds distinguish linearly between proofs over fields of characteristic q and r, q 6= r, and more generally distinguish linearly the rings Zq and Zr where q and r do not have the identical prime factors. Supported in part by international grant INT-9600919/ME-103 from the NSF (USA) and the MSMT (Czech republic) Supported in part by NSF grant DMS-9803515 Supported in part by NSF grant CCR-9734911, Sloan Research Fellowship BR-3311, and US-Israel BSF grant 97-00188. Supported in part by NSF grant CCR-9457783 and US-Israel BSF grant 95-00238.

Linear gaps between degrees for the polynomial calculus modulo distinct primes