Questions tagged [satisfiability]

Satisfiability (SAT) is the problem of determining whether there is a variable assignment that fulfills a given Boolean formula.

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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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Are approximations to $#P$ gibberish? [closed]

approximations to #P are gibberish the model count in satisfiability (#P) implies straightforward access to a vast empire inside the logic of truth including N Boolean variables in a formula with N ...
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Compact representation for quantified boolean formula

I got black-box (too big to analyze) boolean formula f(...) with 3 sets of input arguments: $x_1... x_i, y_1... y_j, z_1... z_k$. And I want to find such values for x-arguments that for every y-...
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Reduction from the SAT problem to the NAE-SAT problem

I study complexity and computation independently. I have a problem that I can not solve. That's the problem: For the SAT problem, there is a version in which we receive as input phrase $\varphi$ in ...
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How to design an unbounded Monte Carlo algorithm for SAT(Boolean Satisfiability Problem) problem?

I want the algorithm to be in polynomial time and the correct answer rate is 0.5 or more. (True / false judgment is polynomial time) All the methods I think of take exponential time(2^n). Can anyone ...
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1answer
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SAT formula for connected graphs on the grid

In the answer to an earlier question "SAT algorithm for determining if a graph is disjoint" a formula is constructed that is satisfiable iff a given graph is connected. The formula uses a ...
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1answer
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Number of queries for $NP^{NP}$

So a few days ago my lecturer told us that for every nondeterministic polynomial time oracle machine $M$, there is a nondeterministic polynomial time oracle machine $N$ that gives us $L(N^{3-SAT}) = L(...
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Is there a $L$-complete variant of SAT?

Many complete problem of different class of complexity has SAT variant. Like 3-SAT or $k$-SAT is $NP$-complete, Horn-SAT is $P$-complete, 2-SAT is $NL$-complete, and so on. So I was wondering if there ...
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Why is it useful to transform 0-1 integer programming problem into SAT problem?

There are several researches studying translating 0-1 integer programming into CNF form. For example, this paper and this C++ library. As the lecture notes here goes, translating 0-1 integer ...
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Computational complexity of dividing a set of constraints into a minimum number of satisfiable clusters

I am looking for the computational complexity of the following problem. Divide a given set of constraints into a minimum number of satisfiable clusters such that the constraints within the same ...
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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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Incomplete definition of function- first order logic

Let $\Sigma=\{c,f^1,R_1^2,...,R_k^2\}$ where $c$ is constant, $f$ is one argument function, and $R_i$ are binary relations. Let $\Sigma_2=\{c,g^2,R_1^1,...,R_k^1\}$ where $c$ is constant, $g$ is two ...
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NP-Hardness of Half-SAT (at least half clauses)

I'm solving Problem 14.14 of What can be computed?. 14.14 Consider the computational problem HALFSAT defined as follows. The input is a Boolean formula B in CNF. If it is impossible to satisfy at ...
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NP Reduction - Dominating set to SAT

Given a graph G and an integer k , recognize whether G contains dominating set X with no more than k vertices. And that is by finding a propositional formula ϕG,k that is only satisfiable if and only ...
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Is there CIRCUIT-SAT algorithms that slightly depends on gates count?

For 3CNF-SAT problems exists a lot of algorithms that still have exponential complexity, but work faster than brute force. The complexity of this algorithm based on a number of variables or the number ...
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NP-completeness of variant SAT: SAT-5Clauses

I'm solving Problem 14.4 of What can be computed?. 14.4 Define the decision problem SAT-5CLAUSES as follows. The input is a Boolean formula B in CNF. The solution is “yes” if it is possible to ...
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Proving satisfiability using resolution and variable elimination

I don't 100% understand this. But I have a entailment, and I want to prove whether it is satisfiable or not, and I will do this using resolution and variable elimination. Here is the formula: $$ (x_1 \...
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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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Has it been shown or can we show that if $SAT \in P$ then SAT can't be in any complexity class C so that $C \subsetneq P$?

I'm already guessing that the answer is no because we cannot know whether there is a class "in between" already known classes? Or can we? I am very new to complexity theory. Thanks for any ...
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1answer
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How to represent bottom element (integer domains) in SMT formula

I'm doing some work with static analysis and need to represent local variables as SMT formulas. In general this is fairly straight forward, depending on the domain of the static analysis. However, ...
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Multi-Objective Implicit Hitting Set for Multi-Objective MaxSAT

MaxSAT is a problem related to SAT where there is a finite collection of hard and soft clauses which share boolean variables. The hard clauses must be satisfied while the soft clauses have a weight. ...
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55 views

Complexity of All-SAT

All-SAT is the problem of enumerating all satisfying assignments of a boolean formula. All-SAT is different from #SAT, where it suffices to find the number of satisfying assignments without ...
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Looking for prior occurrences of $k$-CNF efficiently translated to coloring?

Has anyone else ever translated 3-cnf (4-cnf) on $N$ variables and $M$ clauses into 4 coloring on $O(M)$ vertices? By taking two variables from a clause, the four boolean combinations correspond to ...
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Is clause learning in SAT parsimonius?

I have a model counting program bob. On some graph coloring formulas, bob got the right answer only after removing clause learning. That is to say, with clause learning, bob sometimes counts ...
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What is the difference between NP and co-NP? [duplicate]

I'm trying to understand the very simple concept of co-NP but I can't figure it out. On wikipedia, it gives the example of SAT and its complement: The complement of any problem in NP is a problem in ...
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1answer
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How is this reduction of 3-SAT to Half-SAT not valid? [duplicate]

I am studying algorithms and there is a question in CLRS called the Half-SAT problem We are given a 3-CNF formula with n variables and m clauses where m is even. We wish to determine whether there ...
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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 ...
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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 ...
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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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1answer
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Not satisfiable 3SAT instance implications

Suppose we have an instance of 3SAT that is NOT satisfiable and we say $S$. If in $S$ there are the following $8$ clauses $\left(a\vee b\vee c\right)\wedge\left(a\vee\bar{b}\vee c\right)\wedge\left(a\...
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Can anyone explain the pigeon-hole encoding method in proportional logic

Someone there who worked with cardinal contraindications within the framework of propositional logic? I have a problem understanding the pigeon-hole method. It is a method of satisfaction. I have been ...
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IF satisfiability problem belonged to P, can the certificate be found efficiently?

IF SAT(satisfiability problem) belongs to P, then is it possible for a certificate of an arbitrary instance of SAT to be found efficiently?
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Reduction between Parity-SAT and approximate counting

Consider two problems as defined here. Approximate counting: Given a Boolean function $f(x)$, for $x \in \{0, 1\}^{n}$, distinguish between the two cases: The number of satisfying assignments for $f(...
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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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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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How often can a learned clause cause this solver to backtrack?

The is an improvement to the X3SAT solver I described in What is wrong with this simple proof of P=NP? I have fixed the flaw found in that solver. Now, I want to know how often the solver described ...
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Is there a Zero-Knowledge proof for SAT?

I know that SAT can be reduced to (3 vertex) Graph colouring, and there is a Zero-knowlegde protocol (ZKP) for graph colouring. However, I am interested in a ZKP that can be performed directly on a ...
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Why is SAT so important in theoretical computer science?

In my Computability and Complexity class, we are focusing on P, NP, NP-complete, and NP-hard problems and the one thing that keeps coming up is the SAT problem, in the context of reduction from one ...
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Complementary for $SAT$

I have tried to find a definition of complementary language to $SAT$, I mean $\overline{SAT}$. But I still confused, in case of $L\in \overline{SAT}$ is it mean: if $\varphi\in L$ then all ...
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Solving largely monotone SAT formulas

I just wonder if solving largely monotone SAT formulas (meaning most clauses do not contain negated literals, but some do) is in any way easier than general SAT formulas? In other words, are there ...
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$k$-SAT completeness proof when $k$ is linear in number of variables

I'm looking at a special version of SAT in which each clause has exactly $n/2$ literals, where $n$ is the number of variables. Can we prove NP-completeness of SAT in this case? I tried reducing 3-SAT ...
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Test suite for SAT solvers

I'm looking for a collection of SAT problems that are usable for a test suite, i.e.: are small/easy to solve, that is, this is not a benchmark but a correctness test suite some satisfiable, some ...
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Show that if $SAT \in P/klog(n)$ then $SAT \in P$

Show that if $SAT \in P/klog(n)$ then $SAT \in P$ Assuming that there is a a constant $k \in \mathbb{N}$ such that $SAT \in P/klog(n)$, I need to prove that $SAT \in P$. Since $SAT \in P/klog(n)$, ...
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Different definitions of Exponential Time Hypothesis

I am reading basics of Exponential Time Hypothesis (ETH). There are two statements for it: Statement 1 There exists no $2^{o(n)}$ algorithm for $3$-SAT, where $n$ is the number of variables. Statement ...
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Which of these properties hold for all FO theories? (but not regarding fragments thereof)

Which of these properties hold for all FO theories? (but not regarding fragments thereof) a. Decidable b. At least expressive as propositional logic c. NP-complete a) Decidable: no, some first order ...
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What is a disequality path in the context of equality graphs?

A path consisting of a number of disequality edges and a single equality edge A path consisting of equality edges A path consisting of a number of equality edges and a single disequality edge A ...
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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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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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Reduce Subset-Sum to Sat

Is there a reduction from SUBSET-SUM to SAT? Just general SAT, not 3-SAT. Also the given multiset S only has positive integers. SUBSET-SUM is defined as follows: Input: a multiset S = { x1 , ... , xn }...
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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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