# Questions tagged [sat]

Questions about the Boolean satisfiability problem from computability and complexity theory. If your question is about the college entrance exam called the SAT, you are on the wrong site.

20
questions

**8**

votes

**0**answers

218 views

### Sum of perfect matching construction

Suppose we have two bipartite graphs $G_1$ and $G_2$ with perfect matching count $P_1$ and $P_2$ respectively then their disjoint union gives a bipartite graph with perfect matching $P_1P_2$.
Is ...

**0**

votes

**0**answers

59 views

### Conjecture: on a regular graph one of $k$-IS or $k$-clique is at most subexponential

Let $G$ be simple connected $d$-regular graph of order $n$.
$\overline{G}$ is $(n-1-d)$-regular, so for one of the graphs
we have degree $\ge n/2$.
Clique in $G$ is independent set in $\overline{G}$,
...

**1**

vote

**0**answers

30 views

### Reduction maximum independent set to MIS in a very dense graph

We got a reduction maximum independent set to MIS in a very dense graph,
or alternatively negative monotone 2-CNF to MAX-ONEs with a formula
with many clauses.
Let $G$ be graph of order $n$ and ...

**3**

votes

**1**answer

482 views

### Is strictly harder than NP-hard cryptography possible?

Looks like there is cryptography based on NP-hard problem, e.g. McEliece cryptosystem. The algorithm is an asymmetric encryption algorithm and is based on the hardness of decoding a general linear ...

**5**

votes

**1**answer

800 views

### Does this prove Collatz is a $\Sigma_1$ problem?

So I got an email from one of my colleagues on the Collatz Conjecture with a link to the article Computer Scientists Attempt to Corner the Collatz Conjecture by Kevin Hartnett in Quanta Magazine.
On ...

**3**

votes

**1**answer

169 views

### Mapping Problems to Boolean Formulas for SAT Solvers

I came across Marijn Heule and Oliver Kullmann's paper on recent techniques in highly efficient SAT solvers. In particular they describe the Pythagorian Triple Problem, which they solved using that ...

**-1**

votes

**1**answer

63 views

### How to encode minimality constraint into SAT? [closed]

How to encode maximality/minimality constraints in SAT or its variants such as MaxSAT or MinSAT? For example, let us say (x1 OR x2) AND (x2 OR x3 OR x4) AND (x4 OR x5) is a formula. I want its ...

**1**

vote

**0**answers

32 views

### Is there an algorithm for this constrained Hypergraph optimization problem?

I'm currently developing an algorithm for computing knot coloring invariants and got to the following question:
Given a set $S$ and a certain hyper-graph $H \subseteq S^3 $, find a decomposition $S = ...

**15**

votes

**3**answers

661 views

### Representing mathematical statements as SAT instances

The following problem (call it THEOREMS) belongs to class NP.
Input: Mathematical statement $S$ (written in some formal system such as ZFC) and positive integer $n$ written in unary.
Output: "Yes" if ...

**2**

votes

**0**answers

58 views

### $3$SAT generation with prescribed number of solutions

Given $n,k\in\Bbb N$ with $0\leq k \leq 2^n$ can we generate an uniformly random instance among all possible solutions of an $n$ variable $3$-SAT instance and exactly $k$ solutions in $poly(n\log k)$ ...

**0**

votes

**0**answers

216 views

### What is wrong with the argument that zero permanent is polynomial?

This Lecture summarizes some well known facts about $\#P$ completeness of permanent.
Given a CNF formula $\phi$ on $n$ variables, they construct
matrix $A$ such that:
$$perm(A)=4^{3m} \#SAT(\phi)$$
...

**0**

votes

**0**answers

239 views

### Does "U-SAT in P" imply "P=NP"

Valiant & Vazirani proved SAT transforms UNIQUE SAT under randomized probabilistic reductions in polynomial time. Calabro et al. showed that UNIQUE k-SAT is as hard as k-SAT. Now the question is, ...

**2**

votes

**0**answers

128 views

### relationship of max-sat and min-cut in theory and practice [closed]

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 ...

**3**

votes

**3**answers

240 views

### What kind of SAT am I dealing with here?

Problem set up: I have a long list of variables, $v_i$ (say about 200 total).
I am given a bunch of Boolean statements as follows:
$$\omega_1\land \omega_2\land \omega_3\land \omega_4\land \omega_5 \...

**6**

votes

**0**answers

149 views

### Complexity of finding three perfect matchings with no edge in common in a bridgeless cubic graph

According to a conjecture:
Conjecture (Fan & Raspaud, 1994) Every bridgeless cubic graph contains three perfect matchings with no edge in common.
Equivalent statement here
Main question:
...

**10**

votes

**1**answer

522 views

### How hard is Heyting satisfiability, i.e. the constructive version of SAT? In particular, is 2-HSAT NL-complete or is it harder?

First of all, is it clear what I mean by $k$-HSAT?
I'm assuming that for $k>2$, $k$-HSAT is NP-complete, but the details of the reductions between $k$-HSAT and $k$-SAT aren't obvious to me.
I'm ...

**0**

votes

**2**answers

695 views

### Generating 3SAT circuit for Integer factorization example

I read somewhere that 3SAT can be used to solve Integer Factorization.
If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let's say you are given ...

**16**

votes

**6**answers

2k views

### SAT and Arithmetic Geometry

This is an agglomeration of several questions, linked by a single observation: SAT is equivalent to determining the existence of roots for a system of polynomial equations over $\mathbb{F}_2$ (note ...

**1**

vote

**1**answer

291 views

### Counterexamples for this algorithm for recognizing lexicographic product of graphs?

Found a possible reduction from recognizing lexicographic product of graphs to 2SAT
(since 2SAT is polynomial, the algorithm is polynomial).
Can't prove completeness of the algorithm and since it is ...

**1**

vote

**0**answers

81 views

### Deciding / Approximating Parity of Small Depth Decision Trees

Let C be a circuit such that:
C: $\{0,1\}^n$ to $\{0,1\}$
the top most gate is a parity gate
all the inputs to the parity gate are small depth decision trees
there is a total of $2^{ log^k n}$ ...