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Questions tagged [satisfiability]

For questions on the subject of "satisfiability", that is, whether there exists an interpretation/model in which a given (logical) formula is true.

A formula is valid if it is true for all values of its terms. Satisfiability refers to the existence of a combination of values to make the expression true. So in short, a proposition is satisfiable if there is at least one true result in its truth table, valid if all values it returns in the truth table are true .

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What is the $3$-SAT problem?

In the hopes of improving my knowledge on the question, could someone outline the inputs and outputs for the 3-SAT problem? It would also be helpful if you could express how this problem differs in structure to SAT, 2-SAT or 4-SAT problems.
nubela
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Solving SAT by converting to disjunctive normal form

The first well-known $NPC$ problem is the Boolean Satisfiability Problem, which has a proof of being $NPC$ done by Cook (Cook-Levin Theorem). The problem can easily be described the following way: In complexity theory, the satisfiability problem…
Yippie-Kai-Yay
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Why does Skolemming not preserve validity?

I'm wondering what exactly is meant when people say "Skolemization preserves satisfiability but not validity". I'm having trouble wrapping my brain around it because I think of Skolemization, when considered as an inference rule, to simply "be an…
Greg Nisbet
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Why are Hornsat, 3sat and 2sat not equivalent?

I have been reading a little bit about complexity theory recently, and I'm having a bit of a stumbling block. The horn satisfiability problem is solvable in linear time, but the boolean satisfiability problem in general is NP-Hard. So far so good, I…
Tim Seguine
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Why doesn't implication graph work for 3SAT as it does for 2SAT?

I am trying to understand why it is not possible to use implication graphs, that work to solve $2SAT$, to solve $3SAT$ or $kSAT$ in general. Intuitively I think its because implication extends from one variable from one variable to another, with a…
gautam
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Analysis of Schöning's $k$-SAT algorithm

In his paper "A Probabilistic Algorithm for $k$-SAT and Constraint Satisfaction Problems", Schöning gives a randomized algorithm for $k$-SAT. The analysis conditions on the Hamming distance between a fixed true assignment $a^{*}$ and the initial…
Tommy1234
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What is wrong with this decision procedure for 3SAT?

So I came up with a decision procedure for 3SAT which would seem to be completeable in a polynomial amount of time. Naturally, I am assuming it is incorrect, but I don't know where the mistake is. Ok, so given an instance of 3SAT, reduce it to 3…
Tim Seguine
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In satisfiability, what is the difference between the empty clause and the empty clause set?

The empty clause is a clause containing no literals and by definition is false: $c = \{\} = F$ What then is the empty clause set, and why does it evaluate to true?
Danny King
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Is XOR-SAT + $2$-SAT in P?

I read in a paper a proof where you can reduce a $3$-SAT problem into $2$-SAT + HORN-SAT clauses. $2$-SAT + HORN-SAT is therefore, NP-complete. $2$-SAT, HORN-SAT, DUAL HORN-SAT, XOR-SAT are all in P. I would like to know, if there is a Polynomial…
yugikaiba
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Bounds related to satisfiability problem

This question is regarding MAX-E3SAT problem: Given a set of clauses with exactly three literals, find the maximum number of clauses that can be satisfied. The clauses are expressed as disjunctions of three literals. The literals are variables…
Marvin
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What symbol should be used to indicate that two propositions are consistent with each other?

If I have two propositions $p$ and $q$, what is the simplest standard notation for expressing that they are logically consistent with each other—in other words, that no contradiction can be derived from assuming them both. Something like $\,p,q…
SapereAude
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There exists no zero-order or first-order theory for connected graphs

Prove that no zero-order theory (i.e. propositional calculus, without quantification) or first-order theory can describe the "connected graph" (i.e. from any point one can reach each other point in finite steps). The only weapon I know in these…
W.Rether
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Deciding a problem: is it in $NP$, $NPC$ or $P$?

I'd like your help with understanding whether the following problem is in $P$, $NP$, $NPC$. The problem $B$: Input: a $3CNF$ formula which contains more than one clause. output: Can we divide the formula to two $3CNF$ satisfiable clauses? I'd really…
Jozef
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Can SAT instances be solved using cellular automata?

I'm a high school student, and I have to write a 4000-word research paper on mathematics (as part of the IB Diploma Programme). Among my potential topics were cellular automata and the Boolean satisfiability problem, but then I thought that maybe…
cosmicomic
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How to prove that 3-CNF is satisfiable using Hall's marriage theorem?

Given a 3-CNF formula where each variable from variables $x_1,...,x_n$ appears exactly 3 times in different clauses $c_1,...,c_m$, and each clause contains exactly 3 different variables, prove that the formula is satisfiable using Hall's marriage…
Yos
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