2Sat SubClauses and the Hypernodal Structure of the 3Sat Problem
Abstract
Like simpler graphs, nested (hypernodal) graphs consist of two components: a set of nodes and a set of edges, where each edge connects a pair of nodes. In the hypernodal graph model, however, a node may contain other graphs, so that a node may be contained in a graph that it contains. The inherently recursive structure of the hypernodal graph model aptly characterizes both the structure and dynamic of the 3sat problem, a broadly applicable, though intractable, computer science problem. In this paper I first discuss the structure of the 3sat problem, analyzing the relation of 3sat to 2sat, a related, though tractable problem. I then discuss subclauses and subclause thresholds and the transformation of subclauses into implication graphs, demonstrating how combinations of implication graphs are equivalent to hypernodal graphs. I conclude with a brief discussion of the use of hypernodal graphs to model the 3sat problem, illustrating how hypernodal graphs model both the conditions for satisfiability and the process by which particular 3sat assignments either succeed or fail.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:cs/0404038
 Bibcode:
 2004cs........4038P
 Keywords:

 Computational Complexity;
 Artificial Intelligence;
 G.2.1;
 G.2.2
 EPrint:
 16 pages