How Limited Interaction Hinders Real Communication (and What It Means for Proof and Circuit Complexity)

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceeding

Abstract

We obtain the first true size-space trade-offs for the cutting planes proof system, where the upper bounds hold for size and total space for derivations with constantsize coefficients, and the lower bounds apply to length and formula space (i.e., number of inequalities in memory) even for derivations with exponentially large coefficients. These are also the first trade-offs to hold uniformly for resolution, polynomial calculus and cutting planes, thus capturing the main methods of reasoning used in current state-of-the-art SAT solvers. We prove our results by a reduction to communication lower bounds in a round-efficient version of the real communication model of [Krajǐcek '98], drawing on and extending techniques in [Raz and McKenzie '99] and [Ġoos et al. '15]. The communication lower bounds are in turn established by a reduction to trade-offs between cost and number of rounds in the game of [Dymond and Tompa '85] played on directed acyclic graphs. As a by-product of the techniques developed to show these proof complexity trade-off results, we also obtain an exponential separation between monotone-ACi1 and monotone-ACi, improving exponentially over the superpolynomial separation in [Raz and McKenzie '99]. That is, we give an explicit Boolean function that can be computed by monotone Boolean circuits of depth logi n and polynomial size, but for which circuits of depth O(logi1 n) require exponential size.

Detaljer

Författare
Externa organisationer
  • KTH Royal Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)

Nyckelord

Originalspråkengelska
Titel på värdpublikationProceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor295-304
Antal sidor10
ISBN (elektroniskt)9781509039333
ISBN (tryckt)9781509039340
StatusPublished - 2016 dec 14
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, USA
Varaktighet: 2016 okt 92016 okt 11

Publikationsserier

NamnProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
FörlagIEEE
Volym2016-December
ISSN (tryckt)0272-5428

Konferens

Konferens57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
LandUSA
OrtNew Brunswick
Period2016/10/092016/10/11