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# Questions tagged [counting-complexity]

How hard is counting the number of solutions?

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### Solution Clusters and Monotone-2SAT

It is known that generic k-SAT formulas may exhibit the presence of exponentially many solution clusters. Question: Is it true also for Monotone-2SAT formulas? For the definition of cluster, ...
440 views

### Compactly representing the solution set of a SAT instance

This question has risen in my mind after reading András Salamon's and Colin McQuillan's contributions to my previous question Counting solutions of Monotone-2CNF formulas. EDIT 30th Mar 2011 Added ...
991 views

### Is #P contained in PSPACE?

It's obvious that NP $\subseteq$ #P. How about #P $\subseteq$ PSPACE? It strikes me as semi-obvious, since we can check whether an assignment (e.g. for SAT) is a solution in polynomial time (and ...
876 views

### Counting solutions of Monotone-2CNF formulas

A Monotone-2CNF formula is a CNF formula where each clause is composed by exactly 2 positive literals. Now, I have a Monotone-2CNF formula $F$. Let $S$ be the set of $F$'s satisfying assignments. I ...
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### Consequences of #P = FP

Which would be the consequences of #P = FP? I'm interested in both practical and theoretical consequences. From a practical point of view, I'm particularly interested in consequences on Artificial ...
Consider Ising model on graph $G$ with uniform coupling strength $J$ and magnetic field $h$. I say its partition function $Z$ is easy to compute if $Z$ can be deterministically computed to arbitrary ...