Questions tagged [3-sat]
3SAT is a famous special case of the boolean satisfiability problem (SAT).
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Oracle that can only definitively say if an instance is unsatisfiable
Assuming I have an Oracle that takes as input a strictly 3SAT Boolean instance and states whether the instance is satisfiable or not. If it says instance is unsatisfiable then the instance is ...
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6answers
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Can anyone give me an instance of 3SAT with exactly one solution?
I need an instance of 3SAT with exactly one solution but I cannot think of or find one anywhere. Can anyone please give me an example?
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Reducing 3-SAT to restricted 3-SAT
I am trying to show that the following problem is NP-hard.
Input: A boolean function in CNF (conjunctive normal form) such that every clause has at most three literals and every variable appears in at ...
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2answers
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Is there any algorithm for 3SAT problem that is fast and relatively easy to implement?
Here is the description for 3SAT satisfiability problem. I already know about the DPLL algorithm, but it's implementation is pretty complex. I would like some algorithm that is relatively simpler but ...
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1answer
40 views
1-OR-3-SAT is in P
1-OR-3-SAT:
Input: 3-CNF formula $\varphi$
Question: whether there is an assignment $x$ such that in each clause there are one or three true literals.
I need to show that this problem is in $P$. I ...
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1answer
45 views
Showing resolution algorithm for 2SAT is polynomial time
I don't quite understand why the resolution algorithm completes in polynomial time for 2SAT but not 3SAT.
I'm looking at slide 42 of these slides for reference. It is clear that given two clauses of ...
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0answers
20 views
3-OCC-MAX SAT np-complete?
Assuming 3-OCC-MAX SAT is the language of all CNF formulas in which every variable appears in at most 3 clauses. Is this problem NP-Complete? I'm trying to find a karp reduction between SAT and this ...
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1answer
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algorithm for checking satisfiability
In order to prove that SAT is in NP, I need to come up with a polynomial time verfier (an algorithm). The Cooks Levin Theorem uses a non-deterministic Turing machine but that's not what I am looking ...
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1answer
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Is MAX-averageSAT a well-known problem?
Is there any variant of the Boolean SAT or Max-SAT problem that has a flavor of maximizing or minimizing the average of the weights of the satisfied clauses of a WCNF formula? Any literature on an ...
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planar 1-in-3 sat described as a planar graph for independent set
Given a planar 1-in-3 sat formula, can someone reduce that formula into a graph that asks the question when ever there is an independent set for it, that's also planar?
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1answer
110 views
Is Monotone 3-SAT with exactly 3 distinct variables untractable?
I have given the following SAT variation:
Given a formula F in CNF where each clause C has exactly 3 distinct literals and for each C in F either all literals are positive or all literals are negated....
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1answer
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Proof for NP-hardness of simultaneous minimization and maximization of a weighted subset
I am working on a problem defined as the following
Given a set of $n$ elements called $R \subseteq \mathbb{N} \times \mathbb{N}$ and numbers $Z,G \in \mathbb{N}$, where $Z$ is a measure of our ...
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Assuming the Exponential Time Hypothesis is true, what's the fastest possible algorithm that can be produced for NP-complete problems? [duplicate]
Assuming the Exponential time hypothesis is true, what's the fast possible algorithm that can be produced for NP-complete problems?
If 3-Sat takes exponential time, then could it be possible that ...
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21 views
What would the conqesquences of finding a quasi polynomial-time algorithm for 3-Sat?
What would the conqesquences of finding a quasi polynomial-time algorithm for 3-Sat?
Would this result in their being a quasi polynomial-time algorithm for all NP-complete problems?
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1answer
69 views
When does Gaussian elimination solve exact 1-in-3 SAT?
Terms:
A literal is a variable or its negation.
A clause is a set of literals.
An exact 3-in-1 clause is satisfied if an assignment of values to variables results in exactly 1 ...
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CircuitSAT to 1-in-3SAT
This question follows
Unique 3SAT to Unique 1-in-3SAT
Consider an AND gate such that (A ā§ B) = C. It can be trivially expressed in 3SAT with 4 clauses and no extra variables.
$$
(A āØ B āØ \overline{...
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2answers
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Unique 3SAT to Unique 1-in-3SAT
Suppose I have a CNF formula with clauses of size 2 and 3. It has a unique satisfying assignment.
It was made from a binary multiplication circuit where I multiplied two primes numbers A and B such ...
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1answer
35 views
Unique 1-in-3 SAT
Suppose I have a CNF formula with clauses of size 2 and 3. It has a unique satisfying assignment.
I know the value of each bit of the unique assignment because it was made from a binary ...
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1answer
164 views
How to prove finding two paths that are at least k edges apart is NP-hard?
Let $G=(V, E)$ be an unweighted, undirected, and connected graph. Given two start vertices $s_1$ and $s_2$ and two end vertices $t_1$ and $t_2$ is there a path from $s_1$ to $t_1$ and $s_2$ to $t_2$ ...
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How sub-exponential time does $\text{3SAT}$ have to be to make $\text{NP} \neq\text{EXP}$? What else would imply $\text{NP} \neq\text{EXP}$?
The exponential-time hypothesis posits that if $\mathsf{3SAT}$ has NO subexponential time algorithm (i.e. one in $\mathcal O(2^{o(n)})$), then $\mathsf{P}\neq \mathsf{NP}$.
However, I am interested ...
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1answer
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For given reduction f, can show “if f(x) in 4NAE then x in 3SAT”, but not “if x is not in 3SAT then f(x) not in 4NAE”
Claim: $3SAT \le_p 4NAE $, where reduction $f$ is defined as such: given a 3CNF formula $\varphi$, add to each clause a new literal $z$ (where $z$ is same literal for each clause), and return new ...
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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 ...
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1answer
118 views
Time complexities of state-of-the-art SAT solvers with respect to length of the formula
I am learning about DPLL and CDCL SAT solvers, and I know that they have time complexity exponential to the number of variables.
If I am not mistaken, one of the reasons why most believe P does not ...
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1answer
114 views
Finishing degree requirements NP-complete: Choosing 1 element from each set avoiding conflicts
The question, which I have slightly paraphrased to get rid of the fat, is this: There are $k$ areas of study in which you need to take 1 course. For each area of study, there is a set of courses $C_1,...
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1answer
47 views
CNF satisfiability with a bound on number of clauses
Consider the CNF-sat problem with n literals and k clauses. If k scales linearly in n, we get np-completeness (e.g., 3-sat where each literal appears at most 4 times). Do we still get np-completeness ...
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1answer
675 views
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.
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2answers
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Change the structure from 3SAT to 1in3 3SAT
There is a variable set V = {x1,x2,x3} and clause set C1={x1,x2,-x3} C2={x1,-x1,-x2} C3={-x1,-x2,x3} C4={x2,x3,-x3}. For this structure, no matter each variable is positive or negative, the clause can ...
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0answers
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How does the number of clause affect the difficulty of a 3-SAT Problem? [closed]
It was asked here and closed although it is a very specific question witch was exactly answered in several papers. The complexity of 3-SAT problems has a phase transition which reaches the critical ...
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1answer
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Descriptive complexity of 3SAT
lately I'm reading about descriptive complexity, which I find is a fascinating branch of computational complexity.
I found many formulas in $\exists$$SO$ that describe problems with graphs but none ...
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1answer
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3-CNF to “independent form”
Is it possible to convert all logical formulae into a form such that each variable ends up in exactly 1 "factor" of the and operation? ($\wedge$). Any combination of operations is allowed, though the ...
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What is the generating algorithm for the “komb” instances found on satcompetition.org?
For the 2017 and 2018 Random SAT Tracks of the SAT Competition ran by the International Conference on Theory and Applications of Satisfiability Testing there are small, yet difficult, random 3-SAT ...
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0answers
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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 ...
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1answer
69 views
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 ...
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Is a “stacked”, “local” version of 3-SAT NP-hard?
In this previous question, I learned that if each variable in a string $C \in 3\text{-SAT}$ appears only "locally", then finding a satisfying assignment is no longer NP-hard. My question below builds ...
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1answer
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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 ...
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1answer
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Parametrized reduction from 3-SAT to Independent Set to lower bound running time under ETH assumption
I want to prove that, assuming Exponential Time Hypothesis is true, there is no algorithm that solves Independent Set in $2^{o(|V|+|E|)}$ time. I want to apply the following strong parameterized many-...
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2answers
351 views
Proof that POSITIVE-3-SAT is in the complexity class P
I have the following language:
$$\text{POSITIVE-3-SAT} = \{\langle\phi\rangle \mid \phi\text{ is a satisfiable boolean formula in conjunctive normal form,}\\ \text{ in which all clauses consist of ...
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1answer
82 views
Resolution when clauses contain more than 1 complementary literals
Let's assume that we have clauses $(l_1 \lor l_2 \lor l_3), (\neg l_1 \lor \neg l_2 \lor l_4), (l_1 \lor l_2 \lor l_5), (\neg l_1 \lor \neg l_2 \lor l_6)$, where both $l_1$ and $l_2$ are complementary ...
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The NP completeness proof for a variation of the 3CNF-SAT problem
There is a variation of 3CNF-SAT which is called 10-3-CNF-SAT = {<$\Phi$>: $\Phi$ is a satisfiable CNF formula with $\textbf{at most}$ 3 literals per clause and every variable occurs in $\textbf{at ...
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2answers
177 views
Is every X3SAT instance with no cycles satisfiable?
Exactly 1 in 3 SAT (X3SAT) is a variation of the Boolean Satisfiability problem. Given a set of clauses, where each clause has three literals, is there an assignment such that in each clause exactly ...
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0answers
28 views
Reducing SAT to a P problem in polinomial time [duplicate]
Does reducing SAT in polynomial time to a P problem would mean that P = NP?
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1answer
82 views
Fine-grained complexity of 3-CNF formula evaluation
It's well known that 3-SAT is in NP, which means that one can evaluate a 3-CNF formula in polynomial time. However, I was wondering what the tightest upper bound is for formula verification, expressed ...
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1answer
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Why not do these checks on the number of clauses in 3-SAT?
I've been writing a 3-SAT solver for fun and comparing its performance against the solver pycosat. My solver vastly outperforms pycosat in two special cases, where I solve by doing simple, obvious ...
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1answer
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General structure of solutions to 3-SAT circuits
Certain special forms of the SAT problem have solution sets of a special form. For example, given any three solutions to a 2-SAT circuit, their bitwise median is also a solution. Likewise, given any ...
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1answer
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2SAT Problem using Implication Graph
I was doing a practice question. As you can see below there is an Implication graph. To check whether the problem is satisfiable, I checked whether there were any 'bad loops'. To do so, for each ...
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2answers
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What are known 3SAT to 2SAT reductions?
Is there a way to convert a 3SAT formula into a equisatisfiable 2SAT formula? Each method is of interest, even those that grow exponentially.
(So if, for example, my 3SAT formula has 16 variables and ...
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0answers
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USAT, Arora Barak's book
Here on the page 354 Arora and Barak write below the shaded area
"but in fact $f(\phi)$ $\notin SAT$"
and not
"but in fact $f(\phi) \in SAT$"
While in the last line of the shaded area they write
$...
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1answer
331 views
NP-completeness of vertex cover
Show that the following language is NP-complete
$$ L = \{ \langle G,k \rangle \mid \text{$G$ is a graph with a set $S$ of $k$ vertices hitting every edge of $G$}\}. $$
I know I should reduce the ...
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1answer
267 views
Assuming that P=NP - Finding an optimal algorithm for 3SAT
Let assume that P=NP so we have both search and decision algorithms for 3SAT at polynomial time.
Can you help me to find an optimal algorithm for optimize 3SAT, i.e.: to find the maximum number of ...
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1answer
950 views
3-SAT reduction to jobs scheduling problem (np-completeness)
In this paper with the title of "NP-Complete Scheduling Problem" by J. D. Ullman, I am trying to understand the reduction from 3-SAT problem to a scheduling problem in order to prove the later is also ...
