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Questions tagged [3-sat]

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

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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 ...
entangled_photon's user avatar
4 votes
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Tseitin formula on 2-connected graph

How can we prove that for $\\\\$ every $\\\\$ 2-connected graph G with an odd number of vertices, the unsatisfiable Tseitin formula for it is minimally unsatisfiable, that is, if we remove even a ...
David's user avatar
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Resolution on weakening rule by derived clause

How to prove that every clause that is implied by the input formula (learned or not) can be derived using resolution with weakening rule: $\frac{C} {C \vee D}$ (A clause $C$ is implied by $F$ if for ...
A. H.'s user avatar
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How fast can we make generalized k-SAT?

Suppose a generalized version of k-SAT where the usual clauses (disjunctions of literals) are generalized to arbitrary Boolean functions of k variables. (For example, $(x \oplus (y \land z)), ((x \...
A. H.'s user avatar
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2 votes
2 answers
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How to find a satisfying assignment in polynomial time without the use of randomness?

Assume that we are given a formula in 3-CNF such that at least 1% of the complete assignments satisfy it. My question is how to find a satisfying assignment in polynomial time without the use of ...
S. M.'s user avatar
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The parameterized complexity of Weighted-CNF-SAT parameterized by the number of clauses

What is the parameterized complexity of Weighted-CNF-SAT, when parameterized by the number of clauses? Input: A CNF formula $\phi$ with $m$ clauses and $n$ variables, and an integer $k$. Parameter: $m$...
user3445340's user avatar
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Computational Learning Problem: 3-DNF Reduction

I'm not sure how to solve this problem. Problem statement is: Consider the binary classification problem where X = R d and Y = {0, 1}. Consider the class of Binary classifiers given by intersection of ...
Mr.Zhang's user avatar
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If NP $\subset$ BPP, then NP $\subset$ RP. Confusion about the correctness of Probabilistic Turing Machine

I found the proof of this theorem from https://www.csie.ntu.edu.tw/~lyuu/complexity/2011/20120103s.pdf. Here is the screenshot of the construction of probabilistic Turing machine RP. (https://i.stack....
ltl's user avatar
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Constructing an SAT formula from a Clique graph

We were given this practice question to do in a lecture and its solution afterwards. I have spent hours upon hours trying to understand the solution but still do not understand. From my knowledge when ...
emily-cs's user avatar
0 votes
1 answer
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3sat to clique reduction program

I am searching for a program to convert 3sat to clique problem. I tried following links https://www.geeksforgeeks.org/maximal-clique-problem-recursive-solution/ https://www.geeksforgeeks.org/find-all-...
user's user avatar
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Reference request for Unit Clause Based SAT Reduction Rules

I tested my XSAT solver using the 4 pigeons in 3 holes problem converted to XSAT. The pigeon hole instance I give below had 108 variables and 88 clauses after being converted to monotone XSAT. My ...
Russell Easterly's user avatar
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System of equalities and inequalities is NP-hard using a reduction from 3COLORING

We are require to show that a problem where the input is a system of equalities and inequalities, each involving polynomials of degree at most 2 (with integer coefficients) in n real variables x1, x2,...
staz6's user avatar
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1 vote
1 answer
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Can you transform 3sat (or equivalent) into another satisfiability problem that increases the ratio of solutions to non-solutions

Say I have f(x1,x2,x3,...) where the output is either 0 for all inputs (unsatisfiable) or a variable boolean output of 0 or 1 depending on the input (satisfiable). Let's not consider functions that ...
Benedict Bien's user avatar
2 votes
0 answers
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Modified DPLL for 3-SAT by reducing to 2-SAT

In Boolean Satisfiability of CNF formulae we have $k$-SAT where each clause has at most $k$ literals. It is well known that $k$-SAT is polynomial time reducible to $3$-SAT. It is also well known that $...
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Complexity of this variant of 3-SAT?

This post introduces a new variant of 3-SAT called EQUAL-3-SAT, where the number of 3-Literal clause is equal to the number of variable. Consider the 3-SAT problem where the formula is in conjunctive ...
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Is checking whether a a set of 3-literal clause is satisfiable such that every literal in each clause is either all true or all false NP-complete?

I want to know if checking whether a a set of 3-literal clause is satisfiable such that every literal in each clause is either all true or all false NP-complete? By 3-literal clause, I mean it can ...
Anuj's user avatar
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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<n). Example: for m=6, I've got {a,b,c,d,e,f} = 111010 How to generate these n 3-CNF ...
PeterMacGonagan's user avatar
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2 answers
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Ιf 3SAT reduces to its complement then NP=coNP

Can you please explain to me why the following is true? Ιf 3SAT reduces to its complement then NP=coNP. Thoughts: 3SAT is NP-complete so for every X in NP $X \leq 3SAT$ $\overline {3SAT} $ is NP-...
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Variation of 3-SAT

I already know that SAT and 3-SAT are NP-complete. If in 3-SAT the Boolean expression should be divided to clauses,such that every clause contains at most (in the original problem it says exactly) ...
Hjm's user avatar
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How to reduce 3SAT to TwoOrMoreSAT?

I want to prove, that 2OrMoreSAT is NP-complete. It's defined as follows: A formula is considered strongly satisfiable if there exists a model such that two or more different literals in every clause ...
Rahjid Domal's user avatar
-2 votes
1 answer
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How to prove that it is NP-complete?

I was trying to do this exercise, but I don't know how to solve this problem is NP-complete, what reduction to do. There is a network N of n people, in which every person i is associated with a subset ...
Alfonso Beniamino's user avatar
0 votes
1 answer
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MAX-SAT approximation factor

I am stuck on an exercise that ask the approximation factor of a MAX-SAT approximated algorithm generalized from a MAX-3SAT algorithm MAX-3SAT: set every variable with a random value ($0$ or $1$ each ...
Marcus34's user avatar
3 votes
1 answer
161 views

NP-hard $k$-SAT variant with exactly $\ell$ occurrences per variable

For the purpose of this post, let $k$-SAT be SAT with exactly $k$ literals per clause, as opposed to the more common meaning of at most $k$ literals per clause. With the purpose of proving some ...
J. Schmidt's user avatar
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1 answer
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NP-hard (3-)SAT variant with $n$ clauses and $f(n)$ variables

With the purpose of proving my problem NP-hard, I'd like to reduce from a SAT variant (which of course should remain NP-hard) in which not two parameters are present (typically $n$ clauses and $m$ ...
J. Schmidt's user avatar
2 votes
1 answer
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Why can't 3-SAT be solved efficiently if you convert all clauses (x ∨ y ∨ z) into (u ∨ z) by introducing a variable?

Let $a_i$, $b_i$, etc., be a literal, i.e., a variable or the negation of a variable. 3-SAT concerns formulas in CNF form: $(a_1 \vee a_2 \vee a_3) \wedge \dots \wedge (b_1 \vee b_2 \vee b_3)$ (3-CNF)....
Daniel Donnelly's user avatar
2 votes
1 answer
27 views

I'm trying solve a problem using different versions of SAT, how exactly does mixing SAT affect the hardness of the problem?

I'm trying to solve a problem which I can solve in 3SAT or as a mixed 2,3,4 SAT. I know how hard each of those categories are individually and know the derivations of their hardness individually. But ...
Würthi's user avatar
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Polynomial Reduction from 3SAT

Given an undirected graph $G=(V,E)$ where $V$ is a set of vertices, and $E$ is a set of edges and given a set $D$ where $D \subseteq V $ and $ \forall v \in V \setminus D \: \mid \: \exists w \in D : ...
Emily's user avatar
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Could we know what's the total number of unsatisfiable 3SAT formulas for a given n variables?

given some $n$ variables I would be interested to know what is the count of all 3SAT formulas under $n$ that are unsatisfiable. An example of all 3SAT forumlas under $n=3$ is the following: $$ ( x \...
matan Pleblist's user avatar
3 votes
0 answers
76 views

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 ...
Würthi's user avatar
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2 votes
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Do non-linear dynamical systems have the potential to have an edge on other algorithms when it comes to computing NP-complete problems?

In a recent presentation, I've seen the difficulty of NP-complete/NP-hard problems attributed to the fact that they often have "long range" correlations, or at least they can be interpreted ...
Würthi's user avatar
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1 vote
1 answer
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Why do the 2-SAT techniques do not work for 3-SAT?

i just want to know why the techniques we use to solve the 2-SAT problems cannot be used to solve the 3-SAT problem. So the techniques that i know that help solve 2-sat are the naive on where you just ...
hellothere177's user avatar
-1 votes
1 answer
47 views

Can you help me find some examples of 3co-SAT for 4 variables?

I've been studying the examples of 3co-SAT recently. It's easy to find an example of one variable. $(x_1\lor x_1\lor x_1)\land (\overline{x_1}\lor \overline{x_1}\lor \overline{x_1})$ Examples of 2 ...
lz9866's user avatar
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2 votes
2 answers
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what does **input** mean for the $3SAT$ question? Is it the number of variables $n$ or the number of clauses $m$

We know that $3SAT \in NP$, and the definition of $NP$ is as follows: $NP$ is the class of languages that have polynomial time verifiers. But I have a question: what does input mean for the $3SAT$ ...
lz9866's user avatar
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I need to show that the problem is NP-complete

Double-SAT = {𝜓: 𝜓 has at least two satisfying truth assignments}. Hint: reduce from SAT. Start with a formula 𝜑 and modify it to get a formula 𝜓 so that 𝜑 is satisfibale if and only if 𝜓 has at ...
Jay's user avatar
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1 vote
1 answer
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Enumerating through Turing Machines That Solve Same Problem

Is it possible to enumerate through all the Turing Machines that solve the same given problem? For example, we know that there exists a Turing Machine that finds a satisfying assignment given a 3SAT ...
Alex Johnson's user avatar
1 vote
1 answer
574 views

Proof that 2-sat is P-hard?

i figured out this is what i want to know: in Cook's theorem it is shown that SAT is NP-hard. he shows it by showing that sat is at least as difficult like the word problem for nondet. Polynomial Time ...
heythere's user avatar
2 votes
1 answer
71 views

Complexity of a restricted SAT problem

I am wondering about the complexity of the following SAT related problem: Given a CNF with $n$ clauses containing exactly $k$ literals with the following properties: The intersection of any pair of ...
PhPanda's user avatar
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3 votes
1 answer
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4-SAT but two literals per clause must be true

I'm trying to show that a modified 4-SAT in which at least two literals per clause must be true is NP-complete. I'll call it $4_2$-SAT. I understand the reduction from 3-SAT to 4-SAT, and I know why $...
DeadMuffins's user avatar
3 votes
1 answer
125 views

Find the flaw in the 3SAT solver algorithm

I consider decision version of 3SAT problem. Main idea is to find congruent clauses and construct such maximum formula, which satisfiability/truth table won't be changed. In case of unsatisfiable ...
Alexandr Dorofeev's user avatar
4 votes
1 answer
633 views

3-SAT with atmost 3 variables and variable occuring once per clause

I've stumbled across this problem on CSES https://cses.fi/345/task/E/ and was wondering is it somehow reducible to 2-SAT with given constraints? So, the problem states that you need to solve a 3-SAT ...
ZZT Production DIY and Gaming's user avatar
1 vote
1 answer
273 views

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) \...
PeterMacGonagan's user avatar
0 votes
2 answers
383 views

Integer/prime factorization to 3 SAT

So essentially as the title says, I just want to understand how its done. I have a light idea from my own research, but its failing at one point, and I feel it maybe due to crucial point missing in my ...
khaled sabek's user avatar
2 votes
1 answer
111 views

How to determine if clause will change the satisfiability of the 3SAT formula?

I have satisfiable 3SAT formula like: (x1 or x2 or x3) and (not x1 or x2 or not x3) and some clause which is not in this formula ...
Alexandr Dorofeev's user avatar
0 votes
1 answer
44 views

Can 3-SAT be recognized in less than exponential time?

Obviously it is an open question if $3$-SAT can be decided in a polynomial amount of time. But what results do we know about its recognizabilty? Can $3$-SAT be recognized in a polynomial amount of ...
Craig's user avatar
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1 vote
1 answer
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How to reduce 3-SAT to Set Splitting

I've been reading through Garey & Johnson's "Computers and intractability", and a problem SP4 caught my attention. It is stated as following: Given a collection $C$ of subsets of a ...
Daniil Khlebnikov's user avatar
2 votes
1 answer
286 views

Reducing a CNF formula to a DNF formula in less than exponential time

The easy way is by looking at the $\{0,1\}$-table and construct the corresponding DNF formula from that, but this will take $2^n$ time. I want to do it much more efficiently. My idea is based upon the ...
Mařík Savenko's user avatar
2 votes
1 answer
346 views

What is the maximal length of a CNF formula?

The question is quite short. Let $k$ be a given number. What is the maximal length of $k$-CNF formulae can we compute, over the set of binary variables $\left\{ x_1 ,\ldots, x_n \right\}$? The way I ...
Eric_'s user avatar
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1 vote
1 answer
47 views

Trying to understand 3-SAT self-subsuming process

Trying to understand 3-SAT self-subsuming process I've been studying solver theory and am trying to understand some of the basic concepts that I've been reading. In particular, the idea of self-...
knightgambit's user avatar
2 votes
0 answers
42 views

Non-trivial reduction form SAT to $3$-SAT

Looking for any idea for reduction from $SAT \leq 3-SAT$ where $SAT$ is known to have $d$ variables at most in each clause. I am looking for a reduction in which the resulting formula will not depend ...
Dan D-man's user avatar
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-1 votes
1 answer
75 views

Prove that T3SAT is NP-Complete

Instance: A boolean formula f(x1, . . . , xn) in 3CNF form, with m clauses labelled C1, . . . , Cm. Is there an assignment to x1, . . . , xn such that every third clause is False and all other clauses ...
Joe's user avatar
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