Questions tagged [satisfiability]

Satisfiability (SAT) is the problem of determining whether there is a variable assignment that fulfills a given Boolean formula.

Filter by
Sorted by
Tagged with
0 votes
0 answers
19 views

Effecient encoding of sum equality in cnf+xor

I am wondering as to how to efficiently encode the following subcircuit for a binary satisfiability solver (cnf, and optionally xor clauses, if this helps): ...
user avatar
  • 1,272
0 votes
1 answer
25 views

reducing the word problem for dtm to sat / cnf-sat / 2-sat

word problem: given a language L through a deterministic turing machine, is the word w in the language L? the problem should be decidable, since if there is a deterministic turing machine i can simply ...
user avatar
0 votes
0 answers
16 views

How can I create a reduction from a object state to a SAT problem? [closed]

I have a class with N boolean variables and M states. I wand to create an algorithm which is scaleable for N and M and allow me to check if a new rule in the state transition table can be satisfied. ...
user avatar
3 votes
1 answer
42 views

Why can't $QBF$ be reduced to $SAT$

Let $QBF_k$ be the problem of determining the satisfiability of a formula of the form $Φ = Q_1x_1Q_2x_2 . . . Q_kx_k φ(x_1, . . . , x_n)$. where each $Q_i$ is one of the quantifiers $∀$ or $∃$. So, $Φ$...
user avatar
2 votes
1 answer
57 views

Exponential Time Hypothesis and the input size vs number of variables

According to Exponential Time Hypothesis there does not exist a deterministic algorithm to solve SAT over $V$ variables in time $o(2^V)$. However, let's say the number of literals $n = \omega(poly(V))$...
user avatar
  • 1,349
1 vote
1 answer
28 views

Sum in counting satisfying assignments

Is there a polynomial-time algorithm that computes the sum of two boolean formulas, such that, (#SUM(F,G) = #F + #G), the output satisfying assignments equals the sum of the satisfying assignments of ...
user avatar
1 vote
0 answers
52 views

Is there an alternative method to using Gaussian elimination in order to solve 3-XORSAT

I have a large system of $3$-$XORSAT$ constraints (i.e. up to $3$ variables per constraint) and this can be represented in matrix form as a linear algebra problem $Ax=b$ $mod$ $2$. Solvability (i.e. ...
user avatar
  • 11
1 vote
1 answer
42 views

Proving the NP hardness of two variants of SAT

$k$-$\text{RSAT}$ is a variant of $k$-$\text{SAT}$ where we restrict our attention to formulae in which each variable occurs at most $3$ times, and each literal occurs at most twice. The language $k$-$...
user avatar
3 votes
1 answer
93 views

4-SAT but two literals per clause must be true

I'm trying to show that a modified 4-SAT in which at least two literals per clause must be true is NP-complete. I'll call it $4_2$-SAT. I understand the reduction from 3-SAT to 4-SAT, and I know why $...
user avatar
1 vote
1 answer
27 views

Proving 2SAT is in P vs algorithm for finding a satisfying assignment

I want to understand the proof in the following link that 2SAT is in P. What is the need for the last corollary? Wouldn't be enough to just prove the case for the graph with the help of the path ...
user avatar
  • 113
0 votes
0 answers
15 views

How overapproximation of boolean abstraction function works?

I just found that if original formula is unsat, using boolean abstraction function can result in sat. Clearly this is overapproximate. I wonder if I have contingent formula, does that means my boolean ...
user avatar
4 votes
1 answer
68 views

What are efficient approaches to implement unit propagation in DPLL-based SAT solvers?

I'm trying to decompose deduction steps of DPLL algorithm -- unit propagation and pure literal elimination -- for parallelization. However, I want a baseline and asymptotic analysis to compare to my ...
user avatar
  • 43
3 votes
1 answer
66 views

Find the flaw in the 3SAT solver algorithm

I consider decision version of 3SAT problem. Main idea is to find congruent clauses and construct such maximum formula, which satisfiability/truth table won't be changed. In case of unsatisfiable ...
user avatar
4 votes
1 answer
68 views

3-SAT with atmost 3 variables and variable occuring once per clause

I've stumbled across this problem on CSES https://cses.fi/345/task/E/ and was wondering is it somehow reducible to 2-SAT with given constraints? So, the problem states that you need to solve a 3-SAT ...
user avatar
2 votes
1 answer
44 views

expected running time of Randomwalk for k-SAT

model: gambler ruin theorem. A gambler has $i$ coins initially, in every step, he wins a coin with probability $p$, and loses a coin with probability $1-p$. The expected time that he loses all his ...
user avatar
  • 113
0 votes
1 answer
51 views

Is there a version of the boolean satisfiability problem that has NC complexity?

Boolean satisfiability problem (SAT) is NP-complete by Cook–Levin theorem. (wiki) Horn-satisfiability – given a set of Horn clauses, is there a variable assignment which satisfies them? This is P's ...
user avatar
  • 287
2 votes
1 answer
25 views

Satisfiability of bounded assignment of input variables to CNF formula

Consider a CNF formula $F$ such that all the literals in every clause must be negative ( here is an example : $F$ = ($\bar{x_{1}}$ $\wedge$ $\bar{x_{2}}$) $\vee$ ($\bar{x_{3}}$ $\wedge$ $\bar{x_{4}}$ $...
user avatar
  • 49
2 votes
0 answers
28 views

Quantum Boolean SAT algorithm?

Is there a quantum SAT algorithm, a quantum analogue of the DPLL or CDCL algorithms? Note: I'm not looking for the quantum analogue of the Boolean satisfiability problem (though that would be ...
user avatar
  • 145
2 votes
1 answer
33 views

SAT and #SAT in Quantum

Let us look at the two questions that are NP-complete for a classical computer: Given an arbitrary Boolean expression, find an assignment of variables that evaluates the expression to $0$ (SAT). ...
user avatar
  • 297
0 votes
2 answers
56 views

Integer/prime factorization to 3 SAT

So essentially as the title says, I just want to understand how its done. I have a light idea from my own research, but its failing at one point, and I feel it maybe due to crucial point missing in my ...
user avatar
2 votes
1 answer
33 views

How to determine if clause will change the satisfiability of the 3SAT formula?

I have satisfiable 3SAT formula like: (x1 or x2 or x3) and (not x1 or x2 or not x3) and some clause which is not in this formula ...
user avatar
1 vote
1 answer
29 views

Radius Local Search Algortihm for Max-Sat problem approximating ratio

Assume that in classical Local Search algorithm for MAX-SAT we could flip no more than $r \leq n/2$ variables (let's call it $r$-flip) on every iteration. More precise: on every iteration we're ...
user avatar
0 votes
0 answers
34 views

Polynomial reduction to SAT with a condition

Let L be in NP. Is there always a reduction from L to SAT where atleast m-1 clauses (m being the number of clauses in the CNF formula) can be satisfied? When w is in L it is trivial because the ...
user avatar
0 votes
1 answer
42 views

Can 3-SAT be recognized in less than exponential time?

Obviously it is an open question if $3$-SAT can be decided in a polynomial amount of time. But what results do we know about its recognizabilty? Can $3$-SAT be recognized in a polynomial amount of ...
user avatar
  • 147
1 vote
0 answers
31 views

Conflict Clusters – Another P=NP Proof [closed]

Conflict Clusters – Another P=NP Proof 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 ...
user avatar
2 votes
1 answer
46 views

Reducing a CNF formula to a DNF formula in less than exponential time

The easy way is by looking at the $\{0,1\}$-table and construct the corresponding DNF formula from that, but this will take $2^n$ time. I want to do it much more efficiently. My idea is based upon the ...
user avatar
  • 314
3 votes
1 answer
42 views

Stalmarck's method: x ≡ x → z, does z have to be true?

I have been researching Ståmarck's method 1. In the paper cited here, some rules are given. Rules are made of triplets (x, y, z) such that: y $\to$ z $\equiv$ x where x, y and z are booleans which ...
user avatar
  • 53
4 votes
1 answer
73 views

Attempt to reduce to problem of inner product

The problem of Orthogonality: gives $n$ vectors of dimension $k$ and another set of same, can a pair be found with inner product = $0$? The problem of max product: likewise two sets each $n$ vectors (...
user avatar
2 votes
1 answer
63 views

What is the maximal length of a CNF formula?

The question is quite short. Let $k$ be a given number. What is the maximal length of $k$-CNF formulae can we compute, over the set of binary variables $\left\{ x_1 ,\ldots, x_n \right\}$? The way I ...
user avatar
  • 1
1 vote
1 answer
32 views

Trying to understand 3-SAT self-subsuming process

Trying to understand 3-SAT self-subsuming process I've been studying solver theory and am trying to understand some of the basic concepts that I've been reading. In particular, the idea of self-...
user avatar
2 votes
0 answers
33 views

Non-trivial reduction form SAT to $3$-SAT

Looking for any idea for reduction from $SAT \leq 3-SAT$ where $SAT$ is known to have $d$ variables at most in each clause. I am looking for a reduction in which the resulting formula will not depend ...
user avatar
6 votes
1 answer
421 views

Prove TILING is NP-Complete

I have a homework task to show that $\mathrm{TILING} = \{(T, 1^N) \mid \text{it is possible to cover } N \times N \text{ square with tiles from }T\}$, where $t\in T$ is $C^4$ for some color set $C$, ...
user avatar
  • 63
2 votes
1 answer
41 views

Resolution algorithm does not seem to generate the empty clause

Let's assume I have the following 3 clauses: $\neg T$,$\neg Q$, ($\neg P \lor Q \lor S \lor T)$,$(\neg U, T, \neg S)$,$(\neg U, T, P)$ and I want to see if our KB entails $\neg U$ so I tried to apply ...
user avatar
3 votes
1 answer
97 views

Is 2-SAT over Linear Real Arithmetic in P or NP?

The general boolean satisfiability problem (SAT) is NP-complete, and thus can't be solved in polynomial time (assuming $P \neq NP$). But the special case of 2-SAT is in P, and can be solved in linear ...
user avatar
2 votes
1 answer
32 views

Why proofs of Cook's Theorem assume k is given (n^k for NTM)?

A typical proof of Cook-Levin's Theorem proceeds like this: Suppose problem X is in NP. Then there is an NTM M deciding X in time n^k, for some k. Given a word w, NTM M, and k, we construct a Boolean ...
user avatar
  • 1,016
2 votes
3 answers
168 views

Why can $2$-SAT be solvable efficiently, but $3$-SAT not?

I am aware that 2SAT is polynomial while 3SAT is not, but I am looking for an intuition why its so. After all, even in 2SAT we can attempt all possible truth functions and its $2^n$. So I am hoping ...
user avatar
0 votes
3 answers
44 views

For 3CNF unsatisfiable boolean formulas, does it take exponential time to transform them into disjunctive form?

From the link Solving SAT by converting to disjunctive normal form, I learnt that the algorithm to transform any boolean formula to disjunctive form takes exponential time in worst case. But I have a ...
user avatar
  • 141
0 votes
1 answer
39 views

Algorithm to reduce a Circuit-SAT to NAND-SAT

I am trying to construct an algorithm to reduce OR, AND and NOT gates into NAND-SAT. Can someone give me a hint as to where to start?
user avatar
1 vote
1 answer
82 views

Best compression algorithm for CNF SAT instances in DIMACS

For a CNF SAT instance in the DIMACS format what is the best algorithm to compress it? What is the best algorithm for 3-SAT instances in particular? In 2020 SAT competition used .xz which if I ...
user avatar
  • 11
3 votes
1 answer
145 views

Smallest 3-SAT problem that no one has been able to solve?

In number theory progress is sometimes guided by people stating a specific Diophantine equation that they don't know how to solve. Is there anything similar in the field of Boolean satisfiability? ...
user avatar
  • 31
0 votes
0 answers
42 views

Check if the given satisfying assignment of CNF formula is lexicographically the first

If there is a CNF Boolean formula in $n$ variables then the potential satisfying assignments are the binary strings of length $n$. Given a CNF Boolean formula and a satisfying assignment how ...
user avatar
  • 31
-1 votes
1 answer
60 views

Quasilinear time algorithm for 3-SAT

Is it consistent with the current knowledge that there is an algorithm solving a 3-SAT instance in $n$ clauses in quasilinear time in $n$?
user avatar
  • 31
5 votes
1 answer
225 views

Is there an instance of 3-SAT in less than 100 variables that no one has been able to solve?

In number theory, progress is sometimes guided by people stating a specific Diophantine equation that they don't know how to solve. Is there anything similar in the field of Boolean satisfiability? ...
user avatar
  • 51
0 votes
1 answer
43 views

Boolean formula for graph 3COL

For a given undirected graph $G=(V,E)$ I'm trying to construct a boolean polynomially computable formula $\varphi$ with the following property: $\varphi$ is satisfiable $\iff$ vertices of $G$ can be ...
user avatar
  • 115
2 votes
3 answers
522 views

Why is SAT based on the CNF?

I have been reading up on Boolean logic and, specifically, the Boolean satisfiability problem. I have seen several people mention that the expression must be converted to conjunctive normal form (CNF) ...
user avatar
0 votes
0 answers
28 views

Given a graph and specific VC instance, find number of variables when reducing from VC to SAT

I have question already answered from past exam, and I'm trying to figure where my logic fails. Given a graph find vertex cover of size 2. The question is how many variables are there going to be for ...
user avatar
0 votes
1 answer
65 views

For Turing machines, if the input variables increase, will the state set Q increase ? will the tape alphabet Γ increase?

For Turing machines, if the input variables increase, will the state set Q increase ? will the tape alphabet Γ increase? For example, for the SAT problem, the first question is whether the Boolean ...
user avatar
  • 141
3 votes
1 answer
97 views

How hard is random SAT?

There is plenty of research into the so-called "random SAT" problem, where we basically try to solve SAT instances with clauses chosen "at random" in some sense. There are all ...
user avatar
1 vote
0 answers
22 views

Software/library to generate Ising models for random $k$-sat problems

Could someone point me to a software/library which lets one to generate the Ising model/spin model for random $k$-sat problems or $k$-sat problem of a given structure? I understand that it will be ...
user avatar
2 votes
1 answer
91 views

Reduction from SAT to SAT with exactly k true variables

Let $L$ be defined as follows: $\small L = \{(\phi, k) \mid \phi \in SAT \mbox{ and there is a satisfying assignment for $\phi$ having exactly $k$ true variables} \}$ I am struggling to show that $SAT\...
user avatar

1
2 3 4 5
12