Questions tagged [sat]

SAT stands for the Boolean satisfiability problem.

341 questions
Filter by
Sorted by
Tagged with
385 views

Generate connected induced subgraphs as the satisfying assignments to a SAT instance

I want a SAT instance (in CNF) whose set of satisfying assignments are the connected induced subgraphs of a given input graph. A general solution would be helpful, but I really only need this when the ...
• 141
3k views

Improving Cook's generic reduction for Clique to SAT?

I am interested in reducing $k$-Clique to SAT without making the instance much larger. Clique is in NP so it can be reduced to SAT using logarithmic space. The straightforward Garey/Johnson textbook ...
700 views

Can we confirm that 2-SAT can indeed be transformed into Horn-SAT in this manner?

In the question, Translating SAT to HornSAT, Martin Seymour gives a method due to Joshua Grochow. It transforms 2-SAT into Horn-SAT, by creating a variable for every possible 2-SAT clause. Then, if ...
• 2,100
651 views

How is the MA version of SETH proven to be false?

According to this paper, which discusses a nondeterministic extension of the Strong Exponential Time Hypothesis (SETH), "[…] Williams has recently shown related hypotheses about Merlin-Arthur ...
87 views

#2-SAT or 3-SAT and variable that appears most often

Has anyone explored running times of 3-SAT or #2-SAT given by the occurrences of the highest occurring variable? In other words, if the variable that appears most often appears $x$ times, has anyone ...
• 2,100
687 views

Does solving matrix multiplication in quadratic time imply that SETH is false?

I have a little conjecture that if you could perform matrix multiplication (or solve 3-clique) in $O(n^2 \log(n))$ time, then you could solve CNF-SAT in $O(2^{(1-\epsilon)n})$ time. In other words, ...
• 5,127
1 vote
94 views

Abstract high-level framwork for #SAT

In Abstract DPLL and some other sources there is a high-level framework/ model explained using states and transitions. I need (to build) such a model for a #SAT algorithm. I do know that #SAT ...
• 155
2k views

Is there a non-deterministic linear time algorithm for CNF-SAT?

The decision problem CNF-SAT can be described as follows: Input: A boolean formula $\phi$ in conjunctive normal form. Question: Does there exist a variable assignment that satisfies $\phi$? I'm ...
• 5,127
1 vote
79 views

Complexity of QBF with Restrictions on Models [closed]

Do you know the complexity of the following decision problem? Given a quantified boolean formula (QBF) $\phi$ with $2n$ free variables with $n\in\mathbb{N}$. Is there a satisfying assignment s.t. ...
• 191
311 views

Best SAT upper bounds based on number of clauses

What's the best upper bounds based on number of clauses? In this question shown fastest algorithms for SAT, but there bounds depends from number of variables ( $O(const^n)$ where n is number of ...
45 views

pseudo boolean modularity constraint?

I have a constraint like d >= a ^ b ^ c, where a,b,c,d are binary, ^ is XOR. Is this a pseudo boolean modularity constraint or not? Most Pseudo boolean modularity constraints I saw are with equality, ...
358 views

Space requirements for solving True Quantified Boolean Formulas problem [closed]

I came across this section on the wikipedia page for the TQBF solving problem, and just can't wrap my head about the fact that the space requirement is linear. Moreover, it does not provide any ...
436 views

What is the simplest known solver for a np-complete problem?

Lets define the simpler of two terms as the one with shortest description length on the untyped λ-calculus. Trying to find the simplest solver for a np-complete problem, I've got this: ...
• 3,137
88 views

Complexity of generating a pseudo-Boolean function

A pseudo-Boolean function is a mapping from $\mathcal{B}^n = \{0, 1\}^n$ to $\mathbb{R}$. Following is a pseudo-Boolean function. s_1 s_4 - s_2 s_3 - s_3 s_5 - s_2 s_5 + s_1 + s_4 - s_1 s_3 - ...
• 831
2k views

Limited number of variable occurrences in 1-in-3 SAT

Is there a known result on complexity class of 1-in-3-SAT with restricted number of variable occurrences? I've come up with the following parsimonious reduction with Peter Nightingale, but I want ...
• 428
149 views

Converting Partial Weighted Max SAT to CIRCUIT SAT

I am interested in converting Partial Weighted Max SAT to SAT. I have been recommended to go through CIRCUIT SAT. Partial Weighted Max SAT consists of a set of hard clauses and a set of weighted ...
• 21
194 views

• 627
2k views

Does 1-in-3 SAT remain NP-hard even if every variable occurs both positively and negatively?

The standard problem 1-in-3 SAT (or XSAT or X3SAT) is: Instance: a CNF formula with every clause containing exactly 3 literals Question: is there a satisfying assignment setting precisely 1 literal ...
152 views

Is the computation of a satisfying variable assignment for a Boolean formula $FP^{NP}$-hard?

By the well-known self-reducibility of SAT we can obtain a satisfying variable assignment for a Boolean formula by a polynomial number of calls to an $NP$ oracle (delivering only yes/no answers). Thus,...
266 views

• 686
153 views

What's the upper bounds for #3-SAT circuits?

We have, from this thread on 3-SAT upper bounds, and this answer on #P that the current best upper bounds for 3-SAT is faster than $O(1.31)^n$, and approximately $O(1.64^n)$ for #3-SAT. Can we do ...
• 2,100
1k views

Properties expressible in 2-CNF or 2-SAT

How does one show that a certain property cannot be expressed in 2-CNF (2-SAT)? Are there any games, such as pebble games? It seems that the classical black pebble game and the black-white pebble ...
• 171
312 views

How many sets of vectors can be represented as the solutions of a Horn-SAT instance?

Let the solution space of a SAT instance be the set of Boolean vectors of satisfying assignments of $\{0,1\}$ to the variables (that result in the formula evaluating to TRUE). In other words, a ...
1k views

Best current space lower bound for SAT?

Following on from a previous question, what are the best current space lower bounds for SAT? With a space lower bound I here mean the number of worktape cells used by a Turing machine which uses a ...
2k views

Conversion between k-SAT and XOR-SAT

According to XOR Satisfiability Solver Module for DPLL Integration by Tero Laitinen, we need $2^{n-1}$ CNF clauses to convert an $n$ literal XOR-SAT clause if we do not want to increase the number of ...
• 831
1k views

Consequences of $\oplus \mathbf{P} \subseteq \mathbf{NP}$

I have part of a proof attempt of $\oplus \mathbf{P} \subseteq \mathbf{NP}$. The proof attempt consists of a Karp reduction from the $\oplus \mathbf{P}$-complete problem $\oplus$3-REGULAR VERTEX COVER ...
• 6,842
2k views

Is this variation of TQBF still PSPACE-complete?

Deciding if a quantified boolean formula such as $\forall x_1 \exists x_2 \forall x_3\cdots \exists x_n \varphi(x_1, x_2,\ldots , x_n),$ always evaluates to true is a classical PSPACE-complete ...
• 742
2k views

MAX 1 in 2 SAT Algorithm

The maximum satisfiability problem (Max-Sat) is the problem of finding the maximum number of clauses that can be satisified in a Boolean satisfiability instance. The exactly 1 in 2 Sat problem asks, ...
121 views

extracting/ exploiting similarity of SAT instances by solver

suppose that two SAT formulas on different variables $F_1, F_2$ are given on the input that are known to be true and the problem is to build an algorithm that finds a solution to each. the formulas ...
• 11k
1k views

Definition of Planar 3-SAT

What is the standard definition of Planar 3-SAT? I have seen a number of different definitions. What was the original paper that defined it and proved it to be NP-complete?
• 375
1k views

• 183