Questions tagged [sat]

SAT stands for the Boolean satisfiability problem.

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6
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0answers
163 views

Reverse Skolemization?

I'm wondering if there are any references on "reverse skolemization", that is, converting a formula with functions into one purely consisting of quantifiers by eliminating function applications. I'm ...
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57 views

Determine if a graph has exactly 1 cycle using a SAT solver

I have a connected undirected graph whose edges are either enabled or disabled. I want to create a set of clauses that are SAT iff all enabled edges are part of a single loop. If I assert that each ...
5
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0answers
43 views

Hard family for degree-$D$ MAX-3LIN

Max 3LIN is the problem where one is given a linear system of equations $C$ over $\mathbb{F}_2$ with $3$ variables per equation, and needs to determine the maximum number of equations that can be ...
1
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1answer
109 views

Count satisfying assignments of CNF formulas over all possible negation assignments

Consider the set of all CNF instances that can be generated by adding negations to a single monotone CNF instance. How hard is it to compute the sum of the counts of satisfying assignments for the set?...
6
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1answer
87 views

Axioms of Minimum Size Resolution Refutations

Let $\phi$ be an unsatisfiable CNF formula and let $\Pi$ be a resolution refutation of $\phi$ of minimum size. Let $\psi$ be the subformula of $\phi$ containing the clauses that actually appear as ...
0
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75 views

Given $n\times n$ matrix $A$ with integer entries, find #$k$SAT formula that yields $\mathrm{perm}(A)>0$

For each #$k$SAT instance one can build a matrix $A$ such that $\mathrm{perm}(A) = F(\Sigma)$, where $\Sigma$ is the solution count of the $k$SAT formula and $F$ an easy to invert function. My ...
6
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1answer
235 views

Example problem that is not in $2^{o(n)}$ but could be solved in $O(2^{cn})$ for any $c > 0$ (suggested by wording of ETH)

In the wikipedia article on Time Complexity it is written that: The exponential time hypothesis (ETH) is that 3SAT, the satisfiability problem of Boolean formulas in conjunctive normal form with, ...
4
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0answers
85 views

Is monotone 1-in-3 MAXSAT known to be APX hard?

Monotone 1-in-3 SAT is the problem where each clause of the SAT problem contains exactly 3 positive variables. The goal is to find an assignment such that exactly one variable is true in each clause ...
2
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1answer
100 views

Maximum-minimum satisfiability

In MAX-SAT, given a formula, we want to maximize the number of satisfied clauses: given a formula $\phi = c_1 \cap \cdots \cap c_n$, where each $c_i$ is a disjunction, we want to find the largest $k\...
8
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119 views

Complexity of fractional SAT

Let $(a, k)$-SAT be $k$-SAT with the promise that if there is there is a satisfying assignment, then there is such an assignment that satisfies at least $a$ literals of every clause. Can 3-SAT with $...
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0answers
42 views

How to efficiently verify if a semantic symmetry of a CNF formula is valid?

It is easy to verify that a syntactic symmetry of a CNF formula is correct. Is it also possible to check in polynomial time that a semantic symmetry which is not a syntactic symmetry of a formula is ...
2
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85 views

On the goal of learned clause database reduction in CDCL SAT solvers

Modern SAT solvers frequently reduce the size of their learned clause database in order to keep its size as manageable as possible. This has as effect not to slow down the speed of unit propagations. ...
4
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73 views

Finding a largest symmetrical subset of a k-CNF propositional formula

I have a k-CNF propositional formula $F$ which do not admit any global symmetry i.e. there is no permutation $\sigma$ of its variables such that $\sigma(F) = F$ . I'm interested in finding the largest ...
2
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0answers
52 views

Efficient transformation of clausal proof into resolution proof

Clausal proof is used to certify unsat results of SAT solvers. However the main theoretical results are on resolution proof (for instance, the non existence of a polynomial resolution proof for the ...
2
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0answers
85 views

Transforming a DAG-like resolution proof to a tree like resolution proof

How can a DAG-like resolution proof be transformed to a tree-like resolution proof? Is such a transformation possible in polynomial time?
4
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1answer
76 views

Resolution augmented with the rule of symmetry or the rule of extension

Krishnamurthy (here is the abstract of his paper) showed that resolution augmented with the principle of symmetry forms a proof system (referred to as SR) in which certain formulas (which do not admit ...
-5
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1answer
118 views

What do you think of Bokov's “CNF-SAT is in P” proof? [closed]

There are now several versions of G. V. Bokov's paper "Complexity of the CNF-satisfiability problem", cf. https://arxiv.org/abs/1804.02478 In the most recent version of his paper, the proof is only ...
2
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0answers
36 views

Approximate answer to Max-SMT (bitvector) query

I have a problem that could be completely solved as Max-SMT instances in the theory of quantifier-free bit-vectors, but it apparently is too complex to be tractable with current Max-SMT technology. ...
22
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2answers
2k views

Are there any hard instances of 3-SAT when the clauses can only use literals that are “nearby” each other?

Let the variables be $x_1 , x_2 , x_3 ... x_n$. The distance between two variables is defined as $d(x_a , x_b) = |a-b|$. The distance between two literals is the distance between the corresponding ...
6
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1answer
241 views

What are the consequences of solving XOR 3-SAT in Logspace?

XOR Formulas Consider boolean formulas with connectives $\wedge$ (AND) and $\oplus$ (XOR). Such a boolean formula is a valid instance for XOR SAT if it is a conjunction of $\oplus$-clauses. An $\...
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0answers
94 views

Proof of SAT is complete for NP via first-order reductions

So I have been reading this: https://people.cs.umass.edu/~immerman/book/ch7.pdf I do not understand the proof of theorem 7.16, which says that SAT is complete for NP via first-order reductions. My ...
2
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1answer
521 views

What is best known space requrement for solving SATISFIABILITY problem in exp time

I searched a lot for finding best space requirement algorithm for SATISFIABILITY problem but I didn't find any thing better than brute force that is in DSPACE(n). is there exists better bound? and ...
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1answer
103 views

Can MONOTONE WSAT be in solved in polynomial time?

In the weighted monotone satisfiability problem (MONOTONE WSAT), the input is an n-variable MONOTONE CNF Boolean formula (when there is no a clause with a negated variable) and an integer k, and the ...
1
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1answer
52 views

Is there a standard format for Dependent QBF?

I know there is a standard input format DIMACS for a formula is in conjunctive normal form (CNF) and QDIMACS for quantified Boolean formulas. Is there a similar standard format for the Dependent-QBF (...
5
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108 views

Seminal papers related to SMT theories (particularly QF_ABV)

I am working on an application using Quantifier-Free Bit-Vector/Array satisfiability which may or may not require mucking around with the internals of an SMT solver, and would like to understand what'...
6
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1answer
161 views

Ways to think formally about Satisfiability Modulo Theories

Apologies if this is not a well-thought-out question, but I am interested in formalizing a problem which is ultimately described by a SMT formula in the theory of quantified arrays and linear ...
5
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0answers
187 views

How hard is APPROXIMATE-#SAT?

It is well known that the problem of counting the satisfying assignments of SAT, namely the problem #SAT, is #P-complete. It is also suspected (somewhat less widely) that even deciding SAT should ...
6
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2answers
561 views

a polynomial representation of boolean functions

I came up with this linear transformation to map boolean functions to polynomials and it seems to have some nice properties. I was wondering if there is any reference describing this (and/or similar) ...
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0answers
89 views

How hard is gapped satisfiability?

It is well known that general satisfiability (of polynomially many clauses) is NP-hard, and in fact, it is conjectured that an algorithm deciding instances of SAT takes time nearly $2^n$ on $n$ ...
4
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1answer
426 views

Sparsification Lemma for k-SAT and Exponential Time Hypothesis

According to R. Impagliazzo, R. Paturi and F. Zane, 2001 an instance of $k$-SAT is called sparse if $m = O(n)$ where $m$ denotes the number of clauses and $n$ the number of variables. The ...
0
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1answer
77 views

Reduction from SAT to binary matrix subset problem

I'm trying to understand the answer by @Denis on this question, where he showed a way to reduce from SAT to the binary matrix column subset selection problem. The reason I'm having to post a new ...
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0answers
456 views

Equality Constraints over Sets with Tree Automata

Tree Automata can be used to model sets of values of a Herbrand Universe, for example, to model possible values in a functional program. Systems of subtype constraints over set expressions have ...
7
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1answer
191 views

How to benchmark #2-SAT counting algorithms?

Are there any libraries of #2-SAT instances that are hard to solve with state-of-the-art exact solvers (sharpSAT, cachet, ...)? Alternatively: are there practical ways to generate hard #2-SAT ...
2
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1answer
292 views

Minimum Unsatisfiable Core

Recently in a course I'm taking, we have been learning about the DPLL(T) algorithm for SMT solving. The basic outline goes like this: ...
9
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1answer
236 views

Understanding performance of QFBV SMT solvers

SMT solvers such as Z3 or Boolector use a complex set of heuristics to solve problems. However, this also makes predicting the performance of such a solver for a given problem very hard. My question ...
3
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1answer
257 views

Is deciding whether all satisfying assignments are NAE assignments coNP-complete?

Let the language $L$ consist of the $k$-CNF formulas $\phi$ with the property that any satisfying assignment $x$ of $\phi$ is a Not-All-Equal (NAE) assignment, i.e. every clause of $\phi$ has at least ...
13
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2answers
706 views

Counting the number of satisfying assignments in a POSITIVE CNF-SAT

We know the problem of counting the number of satisfying assignment in a given general boolean formula (CNF-SAT), a given DNF formula, or even a given 2SAT formula is a #P-complete problem. Now, ...
5
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1answer
120 views

Reference request: complexity of $k$-partite $k$-SAT

Let's consider following variation of $k$-SAT that I will call $k$-partite $k$-SAT: given $n$ variables that are divided into $k$ groups and a $k$-SAT formula $\phi$ such that each clause has literal ...
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246 views

Given a Boolean formula, does there exist a small circuit that computes a satisfying assignment?

The 3-SAT problem can be defined as follows: 3-SAT Input: A 3-CNF formula $\phi$ of size $m$ with $n$ variables. Question: Does there exist a variable assignment that satisfies $\phi$? ...
42
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5answers
2k views

Theoretical explanations for practical success of SAT solvers?

What theoretical explanations are there for the practical success of SAT solvers, and can someone give a "wikipedia-style" overview and explanation tying them all together? By analogy, the smoothed ...
9
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0answers
297 views

What are the best known reductions from SAT to CNF-SAT?

Problems Let SAT denote the following problem: Given a boolean formula, does there exist a satisfying assignment? Let CNF-SAT denote the following problem: Given a ...
10
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1answer
246 views

Is bounded-width SAT decidable in logspace?

Elberfeld, Jakoby, and Tantau 2010 (ECCC TR10-062) proved a space-efficient version of Bodlaender's theorem. They showed that for graphs with treewidth at most $k$, a tree decomposition of width $k$ ...
3
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2answers
193 views

Hardness of finding roots of a degree $2$ polynomials over $\mathbb{F}_2$

Since every $3$-SAT instance with $n$ variables can be expressed as a degree-$3$ polynomial over $\mathbb{F}_2$ with $n$ unknowns, the NP-hardness of $3$-SAT directly translates to NP-hardness of ...
5
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0answers
75 views

Reference request for a $\Delta_2^P$ satisfiability problem

I am looking for the name and a reference for a $\Delta_2^P$-complete problem that looks like the following Input: A collection of CNF formulas $\phi_i(x_1^i, x_2^i,\dots, x_m^i, z_1, z_2, \dots, z_{...
12
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2answers
695 views

Is SAT a context-free language?

I am considering the language of all satisfiable propositional logic formulae, SAT (to ensure that this has a finite alphabet, we would encode propositional letters in some suitable way [edit: the ...
5
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0answers
293 views

How to do Type Inference using an SMT solver?

I understand that Hindley-Milner Type Inference can be implemented using an off-the-shelf SMT (Satisfiability Modulo Theories) solver? How would this work, for example for a very simple type system (...
7
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0answers
161 views

Converting a Truth Table into k-CNF formula of Minimal Size in Linear Time

Let $T$ be a truth table of a boolean function $f$ on $n$ input bits. More concretely $T$ could be a list of length $2^n$ such that $T[i] = f(bin(i))$, where $bin(i)$ is the binary representation of ...
4
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0answers
178 views

Subexponential algorithms vs separations

Williams (see also slide 29 here) has shown that an $\frac{2^{n}}{n^{10}}$ algorithm for satisfiability of circuits belonging to a class $\mathcal{C}$ imply that $\mathrm{NEXP}\nsubseteq \mathcal{C}$. ...
1
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1answer
619 views

Positive 1-in-3 SAT FPT or Fixed Parameter Intractable

There are a number of satisfiability problems that are difficult to solve even in the fixed parameter sense. For example, Weighted q-CNF Satisfiability is W[1]-complete when parameterized by the ...
28
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2answers
3k views

Do any quantum algorithms improve on classical SAT?

Classical algorithms can solve 3-SAT in $1.3071^n$ time (randomized) or $1.3303^n$ time (deterministic). (Reference: Best Upper Bounds on SAT ) For comparison, using Grover's algorithm on a quantum ...