2 research outputs found
Counting Membrane Systems
A decision problem is one that has a yes/no answer, while
a counting problem asks how many possible solutions exist associated
with each instance. Every decision problem X has associated a counting
problem, denoted by #X, in a natural way by replacing the question
âis there a solution?â with âhow many solutions are there?â. Counting
problems are very attractive from a computational complexity point of
view: if X is an NP-complete problem then the counting version #X is
NP-hard, but the counting version of some problems in class P can also
be NP-hard.
In this paper, a new class of membrane systems is presented in order
to provide a natural framework to solve counting problems. The class is
inspired by a special kind of non-deterministic Turing machines, called
counting Turing machines, introduced by L. Valiant. A polynomial-time
and uniform solution to the counting version of the SAT problem (a
well-known #P-complete problem) is also provided, by using a family
of counting polarizationless P systems with active membranes, without
dissolution rules and division rules for non-elementary membranes but
where only very restrictive cooperation (minimal cooperation and minimal
production) in object evolution rules is allowed