From 3-SAT to \{2+p\},\{3\}-SAT
Mehmet Giritli
Abstract:
k-SAT is the very well studied restriction of the SAT problem which
has attracted much attention due to its NP-complete complexity and
close relation to many practical problems in Artificial
Intelligence. Inherited from its parent, k-SAT is also NP-complete and
many practical problems can be reduced to it efficiently (i.e. in
polynomial time). In this text we introduce a class of problems,
namely {2+p},{3}-SAT, obtained by restricting 3-SAT such that no
variable occurs more than three times in an instance. We show that
there is an efficient transformation which takes every 3-SAT instance
to a {2+p},{3}-SAT instance.
The motivation behind this work is strongly enhanced by our intuition
that the more we restrict the problem, the easier it will get to
reveal the underlying structure of SAT and in particular, of
3-SAT. Moreover, we investigate whether there is a gain obtained by
transforming instances of 3-SAT to {2+p},{3}-SAT, in terms of
computational cost for satisfiability checking. We later show that
although random {2+p},{3}-SAT is distinctly easier than random 3-SAT,
transformed instances are particularly harder than their originating
3-SAT instances.