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### Complexity of finding three perfect matchings with no edge in common in a bridgeless cubic graph

According to a conjecture:
Conjecture (Fan & Raspaud, 1994) Every bridgeless cubic graph contains three perfect matchings with no edge in common.
Equivalent statement here
Main question:
...

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### relationship of max-sat and min-cut in theory and practice

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model:
For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...

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76 views

### Deciding / Approximating Parity of Small Depth Decision Trees

Let C be a circuit such that:
C: $\{0,1\}^n$ to $\{0,1\}$
the top most gate is a parity gate
all the inputs to the parity gate are small depth decision trees
there is a total of $2^{ log^k n}$ ...

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101 views

### What is wrong with the argument that zero permanent is polynomial?

This Lecture summarizes some well known facts about $\#P$ completeness of permanent.
Given a CNF formula $\phi$ on $n$ variables, they construct
matrix $A$ such that:
$$perm(A)=4^{3m} \#SAT(\phi)$$
...

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83 views

### Does “U-SAT in P” imply “P=NP”

Valiant & Vazirani proved SAT transforms UNIQUE SAT under randomized probabilistic reductions in polynomial time. Calabro et al. showed that UNIQUE k-SAT is as hard as k-SAT. Now the question is, ...

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44 views

### Is there any SMT solver which allows a call to another SMT solver?

I have a problem to solve which is likely to be $\mathbf{NP}^{\mathbf{NP}}$-hard. That is, I could solve it if I could take advantage of an instruction such as "assert UNSAT using ...