Open AccessHard Examples for Common Variable Decision Heuristics
Author(s) -
Marc Vinyals
Publication year - 2020
Publication title -
proceedings of the aaai conference on artificial intelligence
Language(s) - English
Resource type - Journals
eISSN - 2374-3468
pISSN - 2159-5399
DOI - 10.1609/aaai.v34i02.5527
Subject(s) - heuristics , heuristic , variable (mathematics) , resolution (logic) , mathematical proof , computer science , polynomial , implementation , task (project management) , mathematics , algorithm , mathematical optimization , theoretical computer science , artificial intelligence , programming language , geometry , economics , management , mathematical analysis
The CDCL algorithm for SAT is equivalent to the resolution proof system under a few assumptions, one of them being an optimal non-deterministic procedure for choosing the next variable to branch on. In practice this task is left to a variable decision heuristic, and since the so-called VSIDS decision heuristic is considered an integral part of CDCL, whether CDCL with a VSIDS-like heuristic is also equivalent to resolution remained a significant open question.We give a negative answer by building a family of formulas that have resolution proofs of polynomial size but require exponential time to decide in CDCL with common heuristics such as VMTF, CHB, and certain implementations of VSIDS and LRB.
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