Questions tagged [3-sat]

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

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Converting 3SAT to TSP

My question is about converting 3SAT to TSP. I want to know what the distance matrix looks like? (Example attached.)
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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)....
2 votes
1 answer
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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 ...
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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 : ...
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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 \...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $3SAT$ ...
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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 ...
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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 ...
1 vote
1 answer
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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 ...
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1 answer
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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 ...
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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 $...
3 votes
1 answer
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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 ...
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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 ...
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1 answer
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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) \...
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2 answers
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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 ...
2 votes
1 answer
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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 ...
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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 ...
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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 ...
2 votes
1 answer
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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? ...
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Parameterized complexity of 3-SAT

Is the 3-SAT problem with $s$ variables and $t$ clauses FPT, parameterized by $s+t$, or W[1]-hard, or para-NP-hard?
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Why can $2$-SAT be solvable efficiently, but $3$-SAT not?

I am aware that 2SAT is polynomial while 3SAT is not, but I am looking for an intuition why its so. After all, even in 2SAT we can attempt all possible truth functions and its $2^n$. So I am hoping ...
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For 3CNF unsatisfiable boolean formulas, does it take exponential time to transform them into disjunctive form?

From the link Solving SAT by converting to disjunctive normal form, I learnt that the algorithm to transform any boolean formula to disjunctive form takes exponential time in worst case. But I have a ...
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1 vote
1 answer
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Best compression algorithm for CNF SAT instances in DIMACS

For a CNF SAT instance in the DIMACS format what is the best algorithm to compress it? What is the best algorithm for 3-SAT instances in particular? In 2020 SAT competition used .xz which if I ...
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3 votes
1 answer
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Smallest 3-SAT problem that no one has been able to solve?

In number theory progress is sometimes guided by people stating a specific Diophantine equation that they don't know how to solve. Is there anything similar in the field of Boolean satisfiability? ...
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Quasilinear time algorithm for 3-SAT

Is it consistent with the current knowledge that there is an algorithm solving a 3-SAT instance in $n$ clauses in quasilinear time in $n$?
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1 answer
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Is there an instance of 3-SAT in less than 100 variables that no one has been able to solve?

In number theory, progress is sometimes guided by people stating a specific Diophantine equation that they don't know how to solve. Is there anything similar in the field of Boolean satisfiability? ...
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3 votes
1 answer
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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 ...
1 vote
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How to convert Bipartite Perfect Matching to SAT?

SAT is $NP$-complete while Bipartite Perfect Matching is in NC under derandomization assumptions. How to convert Bipartite Perfect Matching from balanced bipartites to SAT without Cook-Levin?
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4 votes
1 answer
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Is 3-UNSAT problem coNP-complete?

The 3-SAT problem, i.e. the problem whether a given Boolean formula consisting of clauses of at most 3 literals is known to be NP-complete. Then it’s complement, i.e. whether such a formula is ...
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Three dimensional matching expressed as SAT

The posting in the website Embedding SATISFIABILITY into 3-DIMENSIONAL MATCHING seeks $3SAT$ as a $3$ dimensional matching instance. I am looking to solve the converse problem. How to solve three ...
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Necessary condition for 3-CNF unique satisfiability

I need to iterate through all formulas of 7 variables in 3-CNF which have unique satisfying assignment (1,1,1,1,1,1,1). I could iterate through all formulas which are true under that assignment -- ...
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Show that $3SAT$ is a polynomial reduction on $MSAT$, i.e. $3SAT \leq_p MSAT$ [duplicate]

The exact definition of $3SAT$ and $MSAT$ are as follows: $3SAT :=$ each clause has exactly 3 literals $MSAT :=$ At least half of the literals of every clause are True My intuition was, as we know ...
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Prove that following 3-CNF is SAT

Let $\phi$ be a 3-CNF expression with the properties Every variable can be used at most 3 times No Variable can be used twice in a term Show that you can always choose the truth-value of the ...
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2 answers
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Is the following problem NP-Complete? [closed]

3SAT with the additional condition that exactly 1 or 3 literals must evaluate to 1.
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Minimal unsatisfiable core algorithm

Wikipedia says that There are several practical methods of computing minimal unsatisfiable cores. but I cannot find any. I suppose that “practical methods” means polynomial algorithms. Be careful, a ...
2 votes
1 answer
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Padding a 2SAT clause

In http://web.mit.edu/neboat/www/6.046-fa09/rec8.pdf, I see that they pad a 2SAT clause $(x\vee y)$ to make it a 3SAT clause by writing $(x\vee y\vee p) \wedge (x\vee y\vee \neg p)$. Why doesn't $(x\...
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NOT satisfiable 3SAT instance certificate

Given a NOT satisfiable 3SAT instance, that we say $S$. Suppose that $M$ is a minimal subset of clauses of $S$ such that $M$ is NOT satisfiable. Say $X$ the subset of variables of $S$ that belong to ...
1 vote
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Which features can be considered for neural network based SAT solving?

I'm trying to implement SAT solver, based on backtracking algorithm and BCP. This SAT solver is trying to pick one literal from each clause, from 3-CNF SAT instances. I've implemented a neural network ...
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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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6 answers
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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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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 ...