Abstract
ABSTRACTWe study an Achlioptas‐process version of the randomk‐SAT process: a bounded number ofk‐clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well‐studied area of probabilistic combinatorics (Achlioptas processes) to random CSP's. In particular, while a rule to delay the 2‐SAT threshold was known previously, this is the first proof of a rule to shift the threshold ofk‐SAT for. We then propose a gap decision problem based upon this semi‐random model. The aim of the problem is to investigate the hardness of the randomk‐SAT decision problem, as opposed to the problem of finding an assignment or certificate of unsatisfiability. Finally, we discuss connections to the study of Achlioptas random graph processes. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 163–173, 2015
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