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The Phase Transition in 1-in-k SAT and NAE 3-SAT Dimitris Achlioptas* Arthur Chtcherba t Gabriel Istrate* Cristopher Moore
 

Summary: The Phase Transition in 1-in-k SAT and NAE 3-SAT
Dimitris Achlioptas* Arthur Chtcherba t Gabriel Istrate* Cristopher Moore
1 Introduction
Determining bounds for the random k-SAT thresh-
old has been an active area of research in recent
years [1, 3]. Yet, in spite of significant efforts, nei-
ther a tight analysis nor the structural properties of
this threshold have been determined.
In this paper we study random instances of two
other canonical variations of satisfiability, 1-in-k SAT
and Not-All-Equal 3-SAT. Like random k-SAT, each
generative model has one parameter c = m/n, the ra-
tio of clauses to variables. Also similarly to random
k-SAT, we focus on "threshold phenomena" occur-
ring in these models and how they might relate to
computational hardness.
For 1-in-k SAT, k ~ 3, we obtain the exact location
of the threshold:
Theorem 1.1 For all k > 3, Cl,k = 1/(2k).
This is the first exact analysis of an NP-complete

  

Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz
Moore, Cris - Department of Computer Science, University of New Mexico

 

Collections: Computer Technologies and Information Sciences