#Positive-2SAT is the problem of counting the number of satisfying assignments to a given Positive 2-CNF formula i.e 2-CNF formulas in which each literal is a positive occurrence of a variable.
The following variant of #Positive 2-SAT is defined as follows :
For example ,We are given a set of variables :
The set of all possible positive 2-literal clauses from the given set of variables are :
- A = [ ab ,ac ,ad ,ae ]
- B = [ bc ,bd ,be ]
- C = [ cd ,ce ]
- D = [ de ]
This version of problem puts restrictions on the inputs such that we can only choose at max only two clause from each set mentioned above to form our set of input clauses.
- A valid input to this variant of #Positive 2-SAT would be (ab ,ac ,bc ,cd) here we have only at max 2 clauses form each set mentioned above.
- An invalid input to this variant of #Positive 2-SAT would be (ac ,ad ,ae ,bc ,cd) this is invalid as we have chosen more than 2 clauses from set A, mentioned above, thus its not a valid input to this version of the problem as we must only choose at max 2 clause form each set.
If its #P-complete for 2-clauses per set at max ,then is the result also true for 1-clause per set at max?
Motivation behind this is to see how the number of solutions changes with respect to the overlap between clauses ,thus I want to know if its #p-complete even for 2-clauses per set ,this will make it easier to see the relation.
We know from this post that this variant is #P-complete where we can select at max only 3-clauses from each set mentioned above ,that's why I wanted to know if this is #P-complete where we allowed to select at max only 2 clauses from each set.
Is this variant of #Positive-2-SAT #P-complete?
To clarify Steven confusion ,The sets are just a special way to classify the set of all possible positive-2-literal clauses with respect to k variables ,and my restriction is that we can make a set of 2-literal clauses as our input to the #Positive-2-SAT but we choose clauses from each set but we may not choose more than 3-clauses from any of these sets.
And any current answer doesn't resolve my question as they seem have to misunderstood the problem statement.