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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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What's an example of an unsatisfiable 3-CNF formula?

I'm trying to wrap my head around an NP-completeness proof which seem to revolve around SAT/3CNF-SAT. Maybe it's the late hour but I'm afraid I can't think of a 3CNF formula that cannot be satisfied (I'm probably missing something obvious). Can you…
user11171
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Implementing the GSAT algorithm - How to select which literal to flip?

The GSAT algorithm is, for the most part, straight forward: You get a formula in conjunctive normal form and flip the literals of the clauses until you find a solution that satisfies the formula or you reach the max_tries/max_flips limit and find no…
Adeiln
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Planarity conditions for Planar 1-in-3 SAT

Planar 3SAT is NP-complete. A planar 3SAT instance is a 3SAT instance for which the graph built using the following rules is planar: add a vertex for every $x_i$ and $\bar{x_i}$ add a vertex for every clause $C_j$ add an edge for every…
Vor
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How to prove that a constrained version of 3SAT in which no literal can occur more than once, is solvable in polynomial time?

I'm trying to work out an assignment (taken from the book Algorithms - by S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani, Chap 8, problem 8.6a), and I'm paraphrasing what it states: Given that 3SAT remains NP-complete even when restricted to…
TCSGrad
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3-SAT for variables appearing 3 times

I've been trying to investigate 3-SAT for variables appearing 3 times and so far I'm getting some mixed answers as to its complexity. For example, https://people.maths.ox.ac.uk/scott/Papers/restricted3sat.pdf says instances of 3-SAT in which…
Paradox
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What is wrong with this simple proof of P=NP?

Exactly 1 in 3 SAT ($X3SAT$) is a variation of the Boolean Satisfiabilty problem. Given an instance of clauses where each clause has three literals, is there a set of literals such that each clause contains exactly one literal from the set. $X3SAT$…
Russell Easterly
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Is a "local" version of 3-SAT NP-hard?

Below is my simplification of part of a larger research project on spatial Bayesian networks: Say a variable is "$k$-local" in a string $C \in 3\text{-CNF}$ if there are fewer than $k$ clauses between the first and last clause in which it appears…
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Randomized algorithm for 3SAT

There is a very simple randomized algorithm that, given a 3SAT, produces an assignment satisfying at least 7/8 of the clauses (in expectation): choose a random assignment. A random assignment satisfies each clause with probability 7/8, and so…
Yuval Filmus
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The relation between 2SAT and 3SAT

Show that proving 2SAT is not NP-Complete would prove that 3SAT is not in P. Or eqivalently - Show that proving 3SAT is in P would prove that 2SAT is NP-Complete. I can see there is an easy reduction from 2SAT to 3SAT and it seems like it is…
Ben Danon
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Generating 3SAT circuit for Integer factorization example

I read somewhere that 3SAT can be used to solve Integer Factorization. If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let's say you are given the number 6, then the factors are 2 and 3.
Jane
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Random restarts for unsatisfiable instances

In the worst case, Boolean satisfiability (assuming P!=NP) takes exponential time. Nonetheless, modern SAT solvers using variants of DPLL, are able to solve enough instances to be useful in practice. One technique used, that has shown good results…
rwallace
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Reduction 3SAT and CLIQUE

Hello everyone this is my first question ever and I apologize if I ask in the wrong manner causing this post to be either closed or deleted. I'm learning Reductions and my professor has asked us to write a paper on reductions (3SAT) When doing the…
Angel
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Forward checking vs arc consistency on 3-SAT

If I were to let the variables be the propositions and, constraint be all clauses being satisfied, which technique would be more effective in solving 3-SAT? Forward checking or arc consistency? From what I gathered forward-checking is $O(n)$, while…
Mark
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Why is 3-SAT used for proving NP-Completeness so often?

I was wondering why 3-SAT is often chosen as the candidate problem from which one reduces from to prove the NP-completeness of another algorithm. I've seen it justified in places such as K&T by We now show that 3-SAT $\leq_p$ Hamiltonian Cycle. Why…
entangled_photon
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How hard is random SAT?

There is plenty of research into the so-called "random SAT" problem, where we basically try to solve SAT instances with clauses chosen "at random" in some sense. There are all kinds of variations of this problem, mostly referring to how the clauses…
Mike Battaglia
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