Questions tagged [sat]

SAT stands for the Boolean satisfiability problem.

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3-clauses from the 3CNF when sufficiently large, has already less than $\epsilon$ fraction of satisfying assignments

I have been struggling to understand this answer, but in this answer in proof section I don't understand this line ""there must exist a large enough family of 3-clauses from the 3CNF, in ...
S. M.'s user avatar
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Short learned clauses for XSAT

Are there any studies about how effective a limited resolution pre-processor is for DPLL-CDCL type SAT solvers? By limited resolution pre-processor I mean a pre-processor that generates short (1,2, or ...
Russell Easterly's user avatar
-1 votes
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Calculation on Sparsification and critical clauses in SAT

I followed from this question. I need to prove, the final result $s_k \leq (1 − \Omega(k^{−1}))s_{\infty}.$ But before prove the final result first I need to prove the $s_k \leq (1 − d/k))s_{\infty}$. ...
S. M.'s user avatar
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Sparsification and critical clauses in SAT

I have been studying the Exponential-Time Hypothesis, ETH, from this paper, there defined $s_k = \inf\{\delta \geq 0 | k\text{-}SAT \in RTIME[2^{\delta n}]\}$. But in that paper's page number 10, I ...
S. M.'s user avatar
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Time complexity of PPZ algorithm

I am trying to understand PPZ (Paturi, Pudlák, Zane) derandomization algorithm for k-SAT, it seems to be very difficult for me. The last line in the below of the image, I don't understand the time ...
A. H.'s user avatar
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Max number of m-clauses NOT subsumed by k-clauses

This question is releated to: Max number of k-clauses such that no two clauses can be resolved? and How often can a clause cause a conflict Assume there are $N$ variables and a maximum size set of $k$-...
Russell Easterly's user avatar
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Max number of k-clauses such that no two clauses can be resolved?

Let $n$ be the number of variables and $k$ the size of the clauses. What is the maximum number of k-clauses such that no two clauses can be resolved to a smaller (less than $k$) clause. I will accept ...
Russell Easterly's user avatar
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Solve 3CNF in Poly-Time with Satisfiability Oracle

The problem: Given an algorithm A which can tell whether any 3CNF formula is satisfiable in poly-time, develop an algorithm B that calculates a solution for the formula, also in poly-time, using A as ...
Dilara's user avatar
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Complexity of Identifying SAT Problems with a Unique Solution from Satisfiable Instances

I am curious about the computational complexity involved in identifying SAT problems that have only one solution from a set of satisfiable SAT instances. input and output: input: A satisfiable cnf ...
Jxb's user avatar
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Variation of (derandomized) Valiant-Vazirani

I am interested in the following "improvement" of the Valiant-Vazirani reduction. As pointed out here, under the right derandomization assumptions one can obtain a deterministic polynomial-...
Noel Arteche's user avatar
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How often can a clause cause a conflict?

This question is about DPLL+CDCL algorithms. How often can a clause cause a conflict? I want to use a specific algorithm. Assume a DPLL+CDCL SAT solver using a fixed variable order. Variables and unit ...
Russell Easterly's user avatar
5 votes
2 answers
226 views

Can CDCL Algorithm Derived Conflict Clauses Always Be Obtained Through Resolution from an Unsatisfiable CNF Formula?

I have a question regarding the Conflict-Driven Clause Learning (CDCL) algorithm applied to an unsatisfiable CNF formula $F$. Specifically, can all the conflict clauses learned by the CDCL algorithm ...
Jxb's user avatar
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17 votes
2 answers
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Is there a SETH (Strong Exponential Time Hypothesis) for CSP (Constraint Satisfaction Problem)?

The Constraint Satisfaction Problem I mentioned is similar to CNF-SAT: A variable can take values from some finite domain $D$ where $|D| = d$. A literal of variable $x$ is an expression of the form $x\...
Junqiang Peng's user avatar
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Certifying the promise in hard promise problems

Do we happen to know of any promise problems where the problem is both conditionally hard (say, NP-hard) while simultaneously being able to certify that the instance satisfies the given promise? For ...
Noel Arteche's user avatar
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Using Simplex for Difference Logic

I'm interested in what happens when using the Simplex algorithm on Difference logic, inspired by problem 5.4 in Kroening and Strichman's Decision Procedures. Clearly, in this case, all constraints of ...
Jova's user avatar
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Methods for Determining the minimal Width of Resolution Refutations for CNF Formulas

Recall that the width of a resolution refutation $R$ of a CNF formula $F$ is the maximal number of literals in any clause occurring in $R$. I am intersting in finding the minimal width of some certain ...
Jxb's user avatar
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13 votes
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Complexity of 1-or-3-in-3-SAT (odd-3-SAT)

Consider a 3-CNF formula $\Phi$, i.e., a conjunction of clauses of 3 literals. I call odd-SAT (or 1-or-3-in-3-SAT) the problem of checking whether there is an assignment of the variables such that ...
a3nm's user avatar
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7 votes
1 answer
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What kind of resolution is CDCL corresponding to?

For an unsatisfiable CNF instance, CDCL will return a resolution refutation. My question : what kind of resolution does it return? tree-like, regular or general?
Jxb's user avatar
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Using a certificate in the proof of NP hardness

Say I wanted to determine that the problem of membership in some language $L \subseteq \{0, 1\}^*$ is NP-hard. Say that I have a reduction $r: \{\text{set of quantifier free formulas} \rightarrow \{0,...
Amar Shah's user avatar
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Can "dense" SAT instances be solved in time $o(2^n)$?

By "dense" I mean instances in which the ratio of variables to clauses is below the critical threshold $2^k\ln2−\frac{(1+\ln2)}2+\epsilon_k$ for $k$-SAT. For general SAT, however, I suppose ...
rus9384's user avatar
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7 votes
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Conversion between NP certificates

This might be a well-known fact, but I can't convince myself of whether this is true. Suppose I have some NP language and two different verifying procedures V and V' for L. For any x in L, is it the ...
Noel Arteche's user avatar
1 vote
1 answer
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Efficient algorithm/ implementation to compute Transitive Closure of a Rule with respect to a Relationship

(Recalling some) Definitions: Fix a finite collection of finite sets: $A_1,\ldots,A_k$. Then relationship $R\subseteq A_1 \times A_2 \times \ldots\times A_k$. (Remark: $A_i$'s need not be distinct.) ...
Inspired_Blue's user avatar
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$NP\subseteq P/poly\implies PH\subseteq P/poly$ [closed]

We know if $NP\subseteq P/poly$ then $PH=\Sigma_2$ Then We want to show that $\Sigma_2-SAT\in P/poly$. Now $$\phi\in \Sigma_2-SAT\iff \exists\ x\in\{0,1\}^{p_1(n)}\ \forall\ y\in \{0,1\}^{p_2(n)},\ \...
Soham Chatterjee's user avatar
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When the tree-like resolution size is the same with general(regular) resolution size?

Background: For an unsatisfiable SAT formulas, the length of a resolution refutaion means the number of clauses in it. It's well known that there exist exponential separation between tree-like and ...
Jxb's user avatar
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2 votes
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95 views

What kind of solver should I use for this hypergraph problem?

I have to list the solutions to the following hypergraph problem: There is a set of nodes, linked by edges that are 2-to-1 and bidirectional. The possible directions are either direct: 2 sources and 1 ...
Denis's user avatar
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3 votes
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Can you compute Shannon expansion of a Boolean formula more efficiently by using a QBF solver?

Maybe this is not enough research level, but I've been scratching my head on it for a while... I'm interested in the Shannon expansion of an existentially quantified Boolean formula of the form: $$ \...
Nicola Gigante's user avatar
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156 views

What's the connection between branchwidth and treewidth

I understand that treewidth and branchwidth are essentially equivalent for a fixed graph, given that $branchwidth(G) = Θ(treewidth(G))$. However, my question pertains to a specific case involving ...
Jxb's user avatar
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Sources that prove solving 2-SAT with DP takes linear time

Would anyone have any sources that describe/an explanation of how solving 2-SAT using dynamic programming takes a linear amount of time? Can't seem to find a text that proves it in detail/formality. ...
wtfamidoing's user avatar
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What advancements in SMT solvers have contributed to progress in the field of theoretical computer science?

SMT solvers use first-order logic on top of SAT solvers with boolean logic. For example, CVC4 is an SMT solver able to accept a rich set of mixed constraints over strings, integers, reals, arrays, ...
hddmss's user avatar
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13 votes
2 answers
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Algebraic equivalent of SAT?

Starting with a simple observation. If $x,y\in\{0,1\}$, then the arithmetic product $x\cdot y$ corresponds to the logical conjunction if we interpret $1$ as true and $0$ as false. But then, for a ...
Nicola Gigante's user avatar
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1 answer
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Require Hamming weight in CNF

I have a SAT problem in conjunctive normal form that I’d like to solve, but I need to add one more condition: for the existing variables $x_1,\ldots,x_n$ the Hamming weight is $k$. (It would be ok to ...
Charles's user avatar
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0 votes
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Regarding UNSAT bechmark of SATLIB found as SAT instance

I found the Satisfiable assignment to one of the UNSAT [SATLIB benchmark][1] instance, specifically uuf50-01.cnf as below answer: [1, 2, 3, 4, -5, -6, -7, -8, 9, 10, -11, 12, 13, 14, -15, -16, 17, 18, ...
vinaych's user avatar
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0 answers
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3SAT instances where no assignment fails to satisfy more than one clause: do they eixst, and what complexity class do they belong in?

Title says it all. I am curious of the 3SAT problem but limited to instances where only one clause is left unsatisfied by any literal assignment. Do such problems exist, and if they do, what is it ...
gdoug's user avatar
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1 vote
1 answer
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Running time of SAT and other EXPTIME algorithms [closed]

I need to propose an algorithm for a NP-hard problem. I use dynamic programming which leads to a running time $O(2^s\cdot n^2), s\leq n.$ The algorithm aims to finding a path in a graph $G(V, E)$ (in ...
user67418's user avatar
0 votes
1 answer
214 views

list of 3-CNF formula that can be solved in polynomial time

Suppose i want to program a 3-SAT solver. I want my solver to first check whether a formula is in the list of 3-CNF that currently known can be solved in polynomial time before resorting to brute ...
LLL's user avatar
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-2 votes
1 answer
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Solving 3-SAT in O(n^6)?

There's an algorithm (published on GitHub) which is claimed to solve any 3-SAT formulation in polynomial time with a complexity of max O(n^6). I would usually brush claims like this away, but having ...
DanielM's user avatar
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2 votes
1 answer
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Short UNSAT Certificates for X3SAT

Exactly 1 in 3 SAT ($X3SAT$) is a variation of the Boolean Satisfiability problem. Given an instance of clauses where each clause has three literals, is there a set of literals such that each clause ...
Russell Easterly's user avatar
1 vote
0 answers
395 views

proof that 2-SAT is P-hard [closed]

i'm doing university work about the 2-sat problem and it is asked why 2-sat is p-hard. We discussed that 3-sat is np-hard and proved this by reduction from cnf-sat to 3cnf-sat. for my work the ...
hellothere's user avatar
2 votes
1 answer
216 views

Complexity of the Complete (3,2) SAT problem?

A complete $k$-CNF formula is a $k$-CNF formula which contains all clauses of size $k$ or lower it implies. Deciding the satisfiability of a complete $k$-CNF formula is clearly a tractable problem ...
Xavier Labouze's user avatar
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2 answers
130 views

Find whether a 3CNF formula with every clause having either all the variables negated or all the variables non-negated is satisfiable

Given a 3CNF formula $\phi$ with the condition that, for every clause of $\phi$, either all the variables are negated or all the variables are non-negated. For example, some allowed clauses are $(x_1\...
Amritanshu singh's user avatar
2 votes
1 answer
319 views

The complexity of 3SAT

It is well known that 3SAT remains NP-complete if every variable occurs exactly twice positively, exactly once negated. then, does 3SAT remain NP-complete if every variable occurs exactly once ...
zhukui bai's user avatar
6 votes
1 answer
143 views

Complexity of maximizing the number of models in a parametric formula

Let $F(x,y)$ be a propositional formula where $x$ and $y$ are vectors of Booleans. We want to maximize over $x$ the number of models of $F$ over $y$. As a decision problem, this becomes: given $F(x,y)$...
David Monniaux's user avatar
0 votes
1 answer
223 views

SAT to k-in-3-SAT reduction

Given a 3-SAT clause. Is there a way to convert 3-SAT to k-in-3-SAT such that: The number of new variables introduced are less than the number of clauses (without adding dummy clauses etc.)? The ...
J.Doe's user avatar
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0 votes
1 answer
167 views

Polynomially solvable 3-SAT problem instances [closed]

Given the 3-SAT problem with $v$ variables and $c$ clauses: Is there a clause to variable ratio for which the 3SAT problem is 'easy' i.e. solvable in polynomial time? We are assuming the 3-SAT ...
TheoryQuest1's user avatar
7 votes
2 answers
283 views

Is there an Upper Bound on Number of Redundant Clauses in a satisfiable $3-SAT$?

For a non-empty $3-SAT$ with $n\geq3$ variables and $T\geq1$ non-identical non-degenerate clauses $C_i$: $$S=C_1 \wedge \ldots \wedge C_T$$ where a non-degenerate clause is one containing $3$ unique ...
Craig's user avatar
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1 vote
1 answer
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3-SAT runtime if an optimal order to eliminate possible solutions is known

As a mental exercise I have been playing around with the 3-SAT problem, but I am having difficulty proving or disproving the usefulness of a current idea that I am playing around with. My current ...
Timothy Schommer's user avatar
1 vote
1 answer
241 views

Can this NP-hardness proof for Super Mario Brothers (and other games) be simplified?

In "Classic Nintendo Games are (Computationally) Hard", a generalized framework based on reducibility of 3-SAT for proving NP-hardness of classic Nintendo games is presented, and several ...
ferris's user avatar
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9 votes
1 answer
314 views

Does Horn SAT (Horn formula in CNF) have an integral polytope?

In some ways, my question is related to this: Is the matching polytope integral? Matching and Horn-SAT are both polynomial time solvable.. So I wonder if there is a Horn polytope, similar to the ...
Shuxue Jiaoshou's user avatar
1 vote
1 answer
146 views

Lower bound for proving a random 3-SAT formula is unsat?

For a random 3-CNF formula with n variables and m clauses, assume this formula is unsat, what is the lower bound for proving it to be unsat? Some results posted in Lower bounds for random 3-SAT via ...
hddmss's user avatar
  • 181
0 votes
1 answer
217 views

Lexicographic Boolean satisfiability

Maximal Satisfying Assignment (Lexicographic Boolean satisfiability / LexMaxSAT), the problem of finding the lexicographically maximum x_1, . . . , x_n ∈ {0, 1}^n that satisfies Boolean formula φ, or ...
user63167's user avatar

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