Questions tagged [satisfiability]

Satisfiability (SAT) is the problem of determining whether there is a variable assignment that fulfills a given Boolean formula.

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Reduction of K-Vertex-Cover to SAT: How to define the constraint?

Overall, one would naturally think that with n different nodes, and for x(1) for example representing node 1, it would be like: x(1)+x(2)+x(3)...+x(n) <= k This would mean that for every possible ...
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How to convert Bipartite Perfect Matching to SAT?

SAT is $NP$-complete while Bipartite Perfect Matching is in NC under derandomization assumptions. How to convert Bipartite Perfect Matching from balanced bipartites to SAT without Cook-Levin?
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Under ETH: $\exists$ Problem unsolvable in $2^{o(n)}$ $\Leftrightarrow^?$ 3-SAT can be represented in linear bits

It is a popular open question if there is a problem unsolvable in $2^{o(n)}$ on inputs with $n$ bits, assuming ETH. I recommend reading that question first. That question states that, assuming the ETH ...
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Simplest transformation from XOR to CNF SAT

What is the simplest way to transfrom $a\newcommand*\xor{\oplus}b=c$ to a CNF SAT expression with minimum number of clauses. The default transformation requires upto 9 clauses. I think we can do much ...
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Is 3-UNSAT problem coNP-complete?

The 3-SAT problem, i.e. the problem whether a given Boolean formula consisting of clauses of at most 3 literals is known to be NP-complete. Then it’s complement, i.e. whether such a formula is ...
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Three dimensional matching expressed as SAT

The posting in the website Embedding SATISFIABILITY into 3-DIMENSIONAL MATCHING seeks $3SAT$ as a $3$ dimensional matching instance. I am looking to solve the converse problem. How to solve three ...
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Converting non-deterministic TM to deterministic TM using poly time SAT solver

Suppose there exist deterministic turing machine $M$ that could solve SAT in polynomial time. How can we construct a deterministic TM $N$ ,by using SAT solver $M$, that take as input a non-...
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Necessary condition for 3-CNF unique satisfiability

I need to iterate through all formulas of 7 variables in 3-CNF which have unique satisfying assignment (1,1,1,1,1,1,1). I could iterate through all formulas which are true under that assignment -- ...
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Compact representation for quantified boolean formula

I got black-box (too big to analyze) boolean formula f(...) with 3 sets of input arguments: $x_1... x_i, y_1... y_j, z_1... z_k$. And I want to find such values for x-arguments that for every y-...
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Reduction from the SAT problem to the NAE-SAT problem

I study complexity and computation independently. I have a problem that I can not solve. That's the problem: For the SAT problem, there is a version in which we receive as input phrase $\varphi$ in ...
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How to design an unbounded Monte Carlo algorithm for SAT(Boolean Satisfiability Problem) problem?

I want the algorithm to be in polynomial time and the correct answer rate is 0.5 or more. (True / false judgment is polynomial time) All the methods I think of take exponential time(2^n). Can anyone ...
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SAT formula for connected graphs on the grid

In the answer to an earlier question "SAT algorithm for determining if a graph is disjoint" a formula is constructed that is satisfiable iff a given graph is connected. The formula uses a ...
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