TY - GEN
T1 - Semantic versus syntactic cutting planes
AU - Filmus, Yuval
AU - Hrubeš, Pavel
AU - Lauria, Massimo
N1 - Publisher Copyright:
© Yuval Filmus, Pavel Hrubeš, and Massimo Lauria; licensed under Creative Commons License CC-BY.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - In this paper, we compare the strength of the semantic and syntactic version of the cutting planes proof system. First, we show that the lower bound technique of Pudlák applies also to semantic cutting planes: the proof system has feasible interpolation via monotone real circuits, which gives an exponential lower bound on lengths of semantic cutting planes refutations. Second, we show that semantic refutations are stronger than syntactic ones. In particular, we give a formula for which any refutation in syntactic cutting planes requires exponential length, while there is a polynomial length refutation in semantic cutting planes. In other words, syntactic cutting planes does not p-simulate semantic cutting planes. We also give two incompatible integer inequalities which require exponential length refutation in syntactic cutting planes.
AB - In this paper, we compare the strength of the semantic and syntactic version of the cutting planes proof system. First, we show that the lower bound technique of Pudlák applies also to semantic cutting planes: the proof system has feasible interpolation via monotone real circuits, which gives an exponential lower bound on lengths of semantic cutting planes refutations. Second, we show that semantic refutations are stronger than syntactic ones. In particular, we give a formula for which any refutation in syntactic cutting planes requires exponential length, while there is a polynomial length refutation in semantic cutting planes. In other words, syntactic cutting planes does not p-simulate semantic cutting planes. We also give two incompatible integer inequalities which require exponential length refutation in syntactic cutting planes.
KW - Cutting planes
KW - Lower bounds
KW - Proof complexity
UR - http://www.scopus.com/inward/record.url?scp=84961639076&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.STACS.2016.35
DO - 10.4230/LIPIcs.STACS.2016.35
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84961639076
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
A2 - Vollmer, Heribert
A2 - Ollinger, Nicolas
T2 - 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
Y2 - 17 February 2016 through 20 February 2016
ER -