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Results tagged with counting-complexity
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user 109
How hard is counting the number of solutions?
14
votes
Accepted
Trees: complexity of counting the number of vertex covers
The complement of a vertex cover is an independent set. Your question is therefore equivalent to asking whether counting independent sets is #P-complete on trees.
The answer to this question is NO, …
- 19.2k
7
votes
Counting solutions of Monotone-2CNF formulas
Some observations, not an answer.
Further to the note to the question, any combination of 3 literals can be expressed in terms of any other combination of literals on the same variables, together wit …
- 19.2k
10
votes
Compactly representing the solution set of a SAT instance
As stated (revision 3), the question has a simple answer: no.
The reason is that even for the highly restricted class of representations given by Boolean circuits with AND, OR, and NOT gates, no nont …
- 19.2k
10
votes
Examples of hardness phase transitions
A particularly striking example of a phase transition is the maximum degree bound for Exactly-$k$-SAT (X$k$SAT), in which each clause contains exactly $k$ distinct literals. The problem flips from be …
- 19.2k
4
votes
When is relaxed counting hard?
Some comments: not an answer.
If $c$ is small enough with respect to the number of vertices in the graph, then the improper colourings will add up to less than 1. Hence there is a trivial reduction …
- 19.2k