# Tagged Questions

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

32 views

### Half-SAT intractability proof

I've been struggling lately with a problem that was in my last complex algorithms exam, and I can't find a solution. The problem is as follows: Half-SAT is a problem where C is a CNF boolean ...
51 views

### Complexity of black box satisfiablty

Say I have a black box $f : 2^n \to 2$ and I want to determine if it is satisfiable. That is, does there exist an input how which it returns true. I am for the purposes of this considering $n$ to be ...
54 views

### DPLL time complexity analysis

Consider the most naïve backtracking for CNF-SAT. It only checks if an assignment satisfies the input formula $\phi$ when all the $n$ variables have values assigned. Let $m$ be the size of $\phi$. ...
23 views

### Shaefer's Dichotomy Theorem [duplicate]

Could you please resolve a confusion with Schaefer's theorem for me? Namely, why does it not imply many problems in P are NP-complete? For example, primality testing surely cannot be reduced to one of ...
55 views

### “Balancing” positive and negative literals in 2-sat

I saw in an answer to this post that it is possible to construct 3-sat clauses with extra variables such that the number of positive and negative literals for each variable are equal. Does anyone ...
81 views

### Complexity of a SAT related problem

Given a set of (propositional) formulae $\Phi$, two formulae $\phi$ and $\xi$, determine whether there exists $\Psi\subseteq \Phi$ such that $\Psi\models \phi$ and $\Psi\not\models \xi$. Question: ...
59 views

### Is weighted XOR-SAT NP-hard?

Given $n$ boolean variables $x_1,\ldots,x_n$ each of which is assigned a positive cost $c_1,\ldots,c_n\in\mathbb{Z}_{>0}$ and a boolean function $f$ on these variables given in the form ...
1k views

### Why do Shaefer's and Mahaney's Theorems not imply P = NP?

I'm sure someone has thought about this before or immediately dismissed it, but why does Schaefer's dichotomy theory along with Mahaney's theorem on sparse sets not imply P = NP ? Here's my ...
45 views

### Can Tarjan's SCC algorithm find satisfying assignment to just 'any' digraph?

Is Tarjan's algorithm capable of finding satisfying assignment to any digraph consists of variables (vertices) and implications (edges)? I know that it solves implication graphs constructed by 2SAT ...
81 views

### Assignment to make formula unsatisfiable

Lets imagine we have a satisfiable formula $F(A_0, A_1,...A_k,S_0,...,S_n)$ The problem to solve is "Is there an assignment for variables $(S_0,...,S_n)$ which will make F unsatisfiable?". One way of ...
41 views

### Conflict Driven Clause Learning backtracking clarification

On the wikipedia page here it describes pretty well the CDCL algorithm (and it seems the pictures were taken from slides created by Sharad Malik at Princeton). However when describing how to backtrack ...
98 views

### Can Circuit Value Problem or HORN-SAT be reduced to PATH problem?

PATH = {(X,R,S,T) | exists an x in S that is admissible} Where R is a relation of X x X x X, S is a unary relation of X and T is a unary relation of X aswell. An x element of X is admissible if it is ...
15 views

### Arthur-Merlin protocol to decide a set size

Please look at the example here at the bottom of page 3, http://www.cs.nyu.edu/~khot/CSCI-GA.3350-001-2014/sol3.pdf Here it seems that the set whose size Arthur is trying to approximate is known in ...
27 views

### Parameterized complexity of Weighted Satisfiability with few variable occurrences

Given an integer $k$ and a Boolean CNF Formula $\phi$, Weighted Satisfiability asks whether $\phi$ is satisfiable by a model of weight $k$, i.e., a model that sets at most $k$ variables to true. This ...
66 views

### The initial NP-complete problem

It is always claimed that Cook and Levin gives the very first NP-complete problem and proof of it. But when I look at the actual proof I think what Cook and Levin did was reduced (or transformed) SAT ...
683 views

### Why does Schaefer's theorem not prove that P=NP?

This is probably a stupid question, but I just don't understand. In another question they came up with Schaefer's dichotomy theorem. To me it looks like it proves that every CSP problem is either in P ...
101 views

### Why don't modern SAT solvers use the notion of a “watched clause”, in the same way they use the notion of a “watched literal”?

Modern SAT solvers use the notion of "watched literals": when a value is chosen for a literal $l$, the solver only checks whether that falsifies clauses with $l$ in them if $l$ is one of the watched ...