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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 .

332 questions
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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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Is 3-SAT useful for anything practical?

If all NP-complete problems can be converted to 3-SAT problems I had an idea that would not solve the NP problem but might be a practical solution. What you could do is simply, make a huge table of 3-SAT problems and whether they are solvable or…
zooby
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List of unsatisfiable cores?

Is there a place I can find a list of known unsatisfiable cores for X variables [no more then 10] in CNF format? Or is there an 'easy' way to find out, say I have 7 variables how many clauses [of the 7 variables] do I need for an unsatisfiable…
FTNomad
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Does a 3SAT instance need to have exactly three terms in each clause?

For example, is (x \/ ~y ) /\ (~x \/ y \/ ~z) valid? I have read conflicting descriptions of 3SAT where some say you must have exactly 3 terms in each clause, others say at most 3. if you have 2 terms (no corresponding z), like in the first clause,…
nixon
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Unsatisfiable $X_3SAT$ Instances

Exactly $1$-in-$3$ SAT ($X_3SAT$) is a variant of the Boolean satisfiability problem. Given a set of clauses, each clause having three literals, is there a set of literals such that each clause contains exactly one literal from this set? $X_3SAT$ is…
Russell Easterly
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CNF formula for exactly one variable is true

Given a list (array) of $n$ variables, what's the algorithm that creates a CNF Formula that will make the SAT solver return assignments in which exactly one variable is true? I know I'm not 100% with the terms here, but I just got this assignment,…
McLovin
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Satisfiability 2 CNF-SAT to 3 CNF-SAT transformation/reduction

This Reduction is trying to prove that 2CNF-SAT is also NP-Complete, after proving 3CNF-SAT is NP-Complete. Why is this reduction wrong? If we had a reduction that given an instance of 2CNF-SAT with k clauses over 'i' number of variables, and we…
MathisLyfe
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Not All Equal 2-Sat Problem

I'm going over past papers for my exam and I came across this question. The only time I have heard of "Not-All-Equal" was as a 3-Sat problem, so I'm wondering if this question does actually mean 2-Sat and if so, could you possibly explain? I dont…
TheRapture87
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Looking for Efficient Encoding Permutations with Boolean Variables

I'm exploring the use of SAT solvers to find a permutation of the numbers 1, 2, and 3, subject to specific constraints. Initially, I considered employing nine variables: $x_{1,1}, x_{1,2}, \dots, x_{3,3}$, where $x_{i,j}$ is true if the number $i$…
NonalcoholicBeer
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Resolution on 3-SAT instance yields in polynomial many resolvents

A SAT instance in CNF with $n$ variables has at most $2^n$ resolvents, therefore the resolution method is not in polynomial time. Considering a 3-SAT instance, we have at most $n^3 + n^2 + n$ many resolvents. Therefore, we can decide 3-SAT in…
John Threepwood
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How to find variable sets of such "one valid" property?

Let's assume that we have to solve a 3-SAT instance (encoded in CNF form) and we are looking for sets of N-variables (smaller are better) that has the following property: When we turn such a set of N-variables into combinations of possible literals…
komorra
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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-subsuming (if I have the correct terminology here) is confusing me. It appears that it's possible to come…
knightgambit
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3-SAT complexity

I'm trying to understand how $3$-SAT problems are assigned complexity to try and get a better understanding of the P vs NP problem. Would a polynomial-time solution to an increasing number of clauses but constant number of distinct literals resolve…
Ben Crossley
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What is the difference between contingent logic and satisfiable logic?

After reading the definitions of both these terms I just confused and I am not able to find good differences between these two. Wikipedia defines satisfiability as "A formula is satisfiable if it is possible to find an interpretation (model) that…
Keshav Ranjan
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Divide and conquer SAT Solver

Are there any SAT solver algorithms which break up a 3SAT sequence of $m$ clauses into $n$ parts, solve these $n$ parts in parallel and then combine the solutions from each part into a final solution for the original problem? I am interested in…
gautam
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