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Questions tagged [3-sat]

3SAT is a famous special case of the boolean satisfiability problem (SAT).

3SAT (3CNF satisfiability) is a particular case of boolean satisfiability problem. It restricts the space of considered formulae to those in 3CNF, that is formulae in conjunctive normal form with at most three literals per clause, e.g. \[(a\lor b) \land (b \lor c \lor d) \land d\]

3SAT is an NP-complete problem and is often used as basis of reduction proofs in complexity theory.

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Are Barthel instances good to use as benchmark for "hard" instances of 3SAT?

I was wondering if, given an algorithm for 3SAT, testing it on Barthel instances would provide a general idea of how well it empirically performs on hard instances. What would other hard instances look like that would perhaps be more…
Würthi
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3-SAT with 3 variable occurences

3-SAT with at most 3 occurences per variable is $\mathsf{NP}$-hard. Now I'll try to solve it using these: Theorem: SAT where all clauses have length 3 and variables occur 3 times, is satisfiable. Double propagation. If there is a clause $(a\lor b)$…
rus9384
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3SAT: Get smallest number of algorithm invocations to get a satisfiable assignment? How should it be done?

My Question is, what is meant with smallest number N. Does it mean I should try every possible constellation of the n variables and put each one of them into the formula φ and then use 3Sat on that? Then it would be 2$^{n}$? Is that meant?
OttoFran
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How many isomorphic 3SAT formulas?

For a 3SAT formula with $n$ variables and $m$ clauses, I am interested in counting the number of isomorphic formulas (isomorphic in the sense that they are logically equivalent and have the same number of variables and clauses). I assume that we…
Lawnmower Man
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3-SAT with negative-literals in each clause

Does a 3-SAT problem, where in each clause there is at least a negative-literal, always has a solution? After looking at it, seems to me that the answer is yes, but maybe there is something I am not seeing.
wallek876
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CNF clause to 3-SAT

How to transform a k-SAT CNF clause into a combination of 2-SAT and/or 3-SAT (1-SAT) clauses? $k>3$ Example 5-SAT: $$ Q = \neg A \lor B \lor C \lor D \lor E $$ $$ \; \; = (X0 \lor X2 \lor X3) \land (Y1 \lor Y2 \lor Y3) \land \; ... $$ Do I have to…
PeterMacGonagan
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Generate a minimum number of clauses in 3-CNF form that give a unique solution

Suppose I would like to generate n clauses, in 3-CNF form, that would give a unique solution for m variables (m
PeterMacGonagan
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