1 research outputs found
Improved Algorithms for the General Exact Satisfiability Problem
The Exact Satisfiability problem asks if we can find a satisfying assignment
to each clause such that exactly one literal in each clause is assigned ,
while the rest are all assigned . We can generalise this problem further by
defining that a clause is solved iff exactly of the literals in the
clause are and all others are . We now introduce the family of
Generalised Exact Satisfiability problems called GXSAT as the problem to
check whether a given instance consisting of clauses with for each clause has a satisfying assignment. In this paper,
we present faster exact polynomial space algorithms, using a nonstandard
measure, to solve GXSAT, for , in time,
time and time, respectively, using polynomial
space, where is the number of variables. This improves the current state of
the art for polynomial space algorithms from time for GXSAT by
Zhou, Jiang and Yin and from time for GXSAT by Dahll\"of and
from time for GXSAT which was by Dahll\"of as well. In
addition, we present faster exact algorithms solving GXSAT, GXSAT and
GXSAT in time, time and time
respectively at the expense of using exponential space