SAT stands for the Boolean satisfiability problem.

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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 ...
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max_sat vs min_cut: theory and practice

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
5
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2answers
140 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 ...
20
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2answers
412 views

best known 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 ...
7
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1answer
140 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 ...
7
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490 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 ...
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183 views

Balanced Boolean function satisfiability

Consider the following problem: Input: A Boolean black-box $U$ of a balanced Boolean function (balanced meaning equal number of satisfying and unsatisfying truth assignments) Output: A ...
22
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2answers
526 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 ...
7
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321 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, ...
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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 ...
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0answers
133 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?
5
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1answer
296 views

Reduction from SAT to 0,1 integer linear program with zero or one solutions

Probably this is well known. There is probabilistic reduction from SAT to Unique SAT (0 or 1 solutions). According to answer and comments derandomizing the reduction would imply $PH \subseteq \oplus ...
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1answer
198 views

Would derandomizing the reduction from SAT to Unique SAT imply $NP$ and $coNP$ are in $\oplus P$?

The Unique SAT problem (USAT) is to determine whether a given formula has a satisfying assignment, when we are guaranteed that it has at most one satisfying assignment. By a theorem ...
3
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1answer
83 views

Satisfiability for various branching programs

Clearly, SAT for CNF, formula, or many classes of boolean circuits have strong significance on the entire theory community. Branching program, or BDD is one of the most basic and popular ...
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0answers
56 views

(co-)Horn formulation of Frankl's union-closed sets conjecture

Based on comments on MO there is simple forumlation of Frankl's union-closed sets conjecture in terms of (co-)Horn. In co-Horn CNF at most one literal is negated in every clause (Horn CNF where every ...
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1answer
93 views

SAT formula specifying that exactly $k$ of $N$ boolean variables are active using less than $N$-choose-$k$ terms

Is there a way to express the condition that exactly $k$ of $N$ boolean variables are active without writing a disjunction of $N$-choose-$k$ terms, i.e., all possible configurations of the $N$ ...
4
votes
3answers
117 views

Remove unneeded atoms in CNF minimalization (SAT preprocessing)

This might be a very basic question. I am interested in all atoms of a propositional formula that can be removed from a particular formula, while the derived formula has the same satisfiability ...
2
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0answers
157 views

Independent Sets that are Odd Covers

I am interested in a certain type of independent set I call an "odd cover". A set of vertices is independent if no two vertices in the set are connected with an edge. A set of vertices is an "odd ...
8
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2answers
174 views

Approximating #P-hard problems

Consider the classical #P-complete problem #3SAT, i.e., to count the number of valuations to make a 3CNF with $n$ variables satisfiable. I am interested in the additive approximability. Clearly, there ...
2
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2answers
112 views

Number of SAT checks that are needed to find all combinations of subset of boolean variables of a propositional formula

Please mind that I sometimes lack formal mathematical knowledge and English is not my first language, so I might miss the right words. Please change the tile if needed. Also, I have choosen this site ...
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0answers
69 views

A self-contained proof that OrdHorn relations are tractable?

I'm currently investigating a family of temporal relations called 'Ordered Horn' ($OH$ for short). This class was introduced in 'Reasoning about Temporal Relations: A Maximal Tractable Subclass of ...
7
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1answer
125 views

$\overline{SAT} \in NTIME(subexp)$?

Is it possible that $\overline{SAT} \in NTIME(\exp(n^{0.9}))$ ? Are there interesting consequences of such containment? Would it contradict the Exponential Time Hypothesis?
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3answers
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Has there been any research on $k$-SAT above the satisfiability threshold?

A well known characteristic of $k$-SAT instances is the ratio of the number of clauses $m$ over the number of variables $n$, i.e., the quotient $\rho = m/n$. For every $k$, there is a threshold value ...
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0answers
146 views

Is SAT in $c^{\sqrt{n}}$ time with preprocessing worthwhile?

We may be able to solve SAT in $c^{\sqrt{n}}$ for $n$ variables and a constant $c$. Now we can suppose that we require a certain amount of preprocessing to get this result. For example, in this ...
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52 views

quadratic constraints in a constraint satisfaction problem

It seems like most constraint satisfaction problems can be posed in terms of SAT. The question is two fold 1) How can any CSP with quadratic constraints be framed as a satisfiability instance 2) Is ...
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82 views

Does this meet the space requirements for the lower 3-SAT bounds?

According to "What are the best current lower bounds on 3SAT?", Ryan Williams has an answer that states that the (time * space) requirements for 3-SAT must meet or exceed $n^{2 \cos(\pi/7) - o(1)}$ ...
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3answers
375 views

If SAT is in PCP, for some constant q, then P = NP

I have seen this statement before, but I haven't really seen a proof of it: If $SAT\in PCP_{1,2^{−q}}[\log(n),q]$, for some constant $q$, then $P = NP$. Now, if $SAT\in PCP_{1,2^{−q}}[\log(n),q]$, ...
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another solution problem (ASP) of integer multicommodity flow: is it NP-complete?

I know that integer multicommodity flow is NP-complete. It was proven in "On the complexity of time table and multi-commodity flow problems" (http://dl.acm.org/citation.cfm?id=1382492) that any SAT ...
18
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2answers
263 views

Polynomial time solvable instances of Max-Sat

The problem Max-Sat ask you to find an assignment of a CNF formula which satisfy as many clauses as possible. For the simpler problem SAT there are many known special cases which can be solved in ...
5
votes
1answer
191 views

Solve multiple instances of SAT with a 2-approximating #SAT query

Assume we have some oracle $A$ such that when given as input a Boolean formula $\phi$, it outputs a 2-approximation to the number of satisfying assignments of $\phi$. If we are given multiple SAT ...
10
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1answer
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Minimum amount of colors preventing an equilateral uniformly colored subtriangle

In the Bundeswettberweb Infomatik 2010/2011, there was an interesting problem: For fixed $n$, find a minimal $k$ and a map $\varphi: \{(i,j)|i\leq j \leq n\}\rightarrow \{1,\ldots,k\}$, such that ...
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1answer
125 views

Hardness of XSAT

The standard NP-hard SAT problem is the problem of Boolean satisfiability of conjunctions of clauses, where clauses are disjunctions of literals. I am interested in the problem of the Boolean ...
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80 views

Variant of Toda's theorem for intermediate levels of the polynomial hierarchy

Is there a version of Toda's theorem for intermediate levels of the polynomial hierarchy ? More precisely, is there any variant of the Toda's theorem that states: Let $\# wSAT$ be the number of ...
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Gradual increase in hardness from P to PH of #SAT

We know that counting the number of solutions to $3-SAT$ is the canonical $\#P-Complete$ problem. Equivalently, it is the canonical $PH-Hard$ problem. However, counting the number of solutions to ...
4
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1answer
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For what k is MAX-2-SAT-k NP-complete?

It is well-known that it is NP-complete to decide whether in a 2-CNF at least s clauses are satisfiable. It also follows from the reduction from 3-SAT-3 that we can suppose that every literal occurs ...
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1answer
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How to go about finding the most “complex” function?

Intro Hi, I'm a hobbyist, with no formal education, tinkering with SAT solving and boolean algebra minimization. So expect bad terminology. I hope you will forgive me I'm asking a wrong question in a ...
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Generalized sequential machine synthesis subject to language equivalence/inclusion and reachability

A generalized sequential machine (GSM) is a generalization of a Mealy machine where on each transition one input symbol is read and 0 or more output symbols are written. As in a Mealy machine, we ...
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Determining if a function is constant or not using period finding

Consider an arbitrary boolean function $$f: {\lbrace 0,1 \rbrace}^n \rightarrow \lbrace 0,1 \rbrace$$ which we write as: $$f(x_1, x_2 ... x_n) $$ where each $x_i$ is a boolean variable We note ...
10
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Is Almost-2-SAT NP-hard?

Is a CNF SAT problem NP hard when the total number (but not the width) of the 3-or-more-term clauses is bounded above by a constant? What about specifically when there's only one such clause?
7
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Random 3-SAT: What is the consensus experimental range of the threshold?

The critical ratio of clauses to variables for random 3-SAT is more than 3 and less than 6, and seems to be commonly described as "around 4.2" or "around 4.25". Mezard, Parisi, and Zecchina prove (in ...
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147 views

Most general form of SAT which is in P

2-SAT is in P. Additionally, a (CNF) SAT-problem is trivially poly-time solvable if no two expressions can be resolved (via Robinson resolution, ie for every pair of disjunctive clauses, they either ...
9
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1answer
258 views

Computational Model in SETH

Impagliazzo, Paturi and Calabro, Impagliazzo, Paturi introduced Exponential-Time Hypothesis (ETH) and Strongly Exponential-Time Hypothesis (SETH). Roughly, SETH says that there is no algorithm which ...
7
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2answers
239 views

SAT in some DTIME always via a constructive proof?

Why can the statement $SAT \in DTIME(n^3)$ not be proven through a non-constructive proof? Intuitively a proof would be a turing machine, which solves this problem in $DTIME(n^3)$, but there are ...
8
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1answer
341 views

Transform a CNF into an equivalent 3-CNF defined on the same variables

(I posted this question on CS ten days ago, with no answer since then - so I post it here.) Any CNF formula can be transform in polynomial time into a 3-CNF formula by using new variables. It is not ...
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2answers
330 views

Questions about special types of partial assignments

Considering the definition "2-SAT: Given a CNF formula whose clauses have exactly 2 literals, does there exist an assignment of $\mathsf{TRUE}$ or $\mathsf{FALSE}$ to the variables that will ...
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323 views

Williams' Method, Natural Proofs and Constructivity

I have some questions on the previous question which is written bellow. Natural Proof and Constructivity : The topic of the previous question Recently, Ryan Williams proved that Constructivity in ...
11
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1answer
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Detecting circuit that's similar in functionality and implementation

Let $x=(x_1,\dots,x_n)$ be a vector of boolean variables. Let $C,D$ be two boolean circuits on $x$. Say that $C$ is similar to $D$ if: $\Pr[C(x) \ne D(x)]$ is exponentially small, when $x$ is ...
14
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5answers
323 views

Unique $k$-SAT benchmarks

This question is probably on the border line between on-topic and off-topic, however I've seen similar questions here, therefore I'll ask it. I'm implementing a Unique $k$-SAT solver, whose input ...
9
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6answers
730 views

variations of SAT

I looked up on the internet, but I could not find any 'big-list' of variants of SAT problem. Apart from the (common) SAT, k-SAT, MAX-kSAT, Half-SAT, XOR-SAT, NAE-SAT what else variants are ...
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Which subproblems of 3SAT are still NP complete?

The problems in the class NP-complete satisfies the property that if any of them is in P, then all other NP-complete problem is in P. The 3SAT is NP-complete, as much as every kSAT with $k\geq 3$. (On ...