A decision problem is a question (in some formal system) whose answer is either "yes" or "no".
Questions tagged [decision-problems]
125 questions
17
votes
0 answers
Fastest way to check existence of solution for a linear system of inequalities
What is the fastest way to check if there exists a solution to the inequality $A x \leq b$, with $A \in \mathbb R^{n \times m}$?
I know this can be checked through the phase 1 of a linear programming algorithm, but I would like to know if there…
Tobia Marcucci
- 739
16
votes
4 answers
Computationally checking if a function is convex
Consider a real-valued function $f : \mathbb{R} \to \mathbb{R}$. Given any $x \in \mathbb{R}$, we can compute $f(x)$. We do not know the analytical form of $f$, and it should be treated as a black box. However we do know that $f$ is first-order…
Adam
- 404
14
votes
2 answers
Does there exist a computer program that is able to determine whether a given function is uniformly continuous?
I was wondering if someone might know whether there exists (or whether it is even possible) for a computer program to process a given function and determine whether it is uniformly continuous.
I have tried to search for a question that might have…
Ang Ming Wen
- 471
9
votes
2 answers
Singularity of a conic combination of rank-$1$ matrices
Given rank-$1$ square matrices $A_1, A_2, \dots, A_n$, determine if there exists $x \in \mathbb R_{>0}^n$ such that
$$ \sum_{i=1}^n x_i A_i = x_1 A_1 + \cdots + x_n A_n $$
is singular, or decide whether none exists (i.e., the positive linear…
M.A
- 450
8
votes
6 answers
How to tell if two matrices are equal up to a permutation?
Given two real rectangular matrices, $A$ and $B$, how can I tell if they are equal up to a permutation of their rows/column without trying all possible permutations?
(This is closely related to the question I asked yesterday, Algorithm to determine…
djangology
- 141
8
votes
3 answers
How to find out whether a linear program is infeasible using the simplex algorithm?
In these notes, finding out whether a linear program (LP) is infeasible via the simplex algorithm is mentioned, but it does not actually go over it. How does one find whether an LP is infeasible using the simplex algorithm?
simplex
- 81
6
votes
1 answer
Characterisation of linearly separable points of a hypercube
Essentially, linearly separable points are just those corners that can be cut off with just one slice as marked out by a hyperplane.
E.g. for a cube, the following 4 points (red) are not linearly separable - no single cut by a plane (tilted at…
mchen
- 595
6
votes
2 answers
How do I determine if a matrix is contained in another matrix?
Is there a clever way of determining if one matrix is contained within another larger matrix? Iterating over the larger matrix to check each item until potential matches show up is straightforward but gets slow for large matrices.
Example, a smaller…
Nick
- 1,320
5
votes
1 answer
Can This Classical-Kleene Combination for Intuitionistic Fragment $\{ \neg, \vee, \wedge \}$ Be Extended to Include $\rightarrow$?
Over a year ago, I worked out a classical-Kleene combination logic that worked to preserve intuitionistic tautologies over the intuitionistic fragment with operators $\{ \neg, \vee, \wedge \}$, which works as follows:
I use $\{ 0, 1, 2 \}$ to…
Joshua Harwood
- 478
5
votes
2 answers
Does decidability imply inconsistency?
I have always thought that according to Gödel's incompleteness problems, every inconsistent theory would be decidable.
This is indicated, here for example: https://en.wikipedia.org/wiki/Decidability_(logic)
There are several basic results about…
jerard
- 51
4
votes
1 answer
How to determine whether a system of linear inequalities has a positive solution or not?
How to determine whether a system of linear inequalities has a positive solution or not?
Is there any poly-time algorithm to do this? Or the best algorithms known are no less complex than algorithms for solving set of linear inequalities?
Michal
- 141
4
votes
0 answers
Minimum spanning forest, for a complete graph.
Given a complete Graph $G(V,E)$ with $|V|=kn$ and weights $w:E→N$ that satisfies "Triangular Inequality". That is, for any $v_1, v_2, v_3 \in V$,$$w(v_1,v_2)\le w(v_1,v_3)+w(v_3,v_2).$$
Can I find the minimum spanning forest $T_1,T_2,…,T_n$ where…
diego.0412
- 81
4
votes
1 answer
Minimum spanning forest, where each tree has the same number of vertices.
Given a connected Graph $G(V,E)$ with weights $w\colon E\to\mathbb{N}$ and $|V|=kn$. How can I find the minimum spanning forest $T_1,T_2, \dots, T_n$ where each tree $T_i$ has exactly $k$ vertices?
I wonder if this problem is P or NP, I am…
diego.0412
- 81
4
votes
1 answer
Presentation of a subgroup of a given index
I am unable to find an explanation of why it is possible to compute a finite presentation of a finite index subgroup in a given finitely presented group. More particularly, if $G$ is a virtually nilpotent group (given by a finite presentation), how…
J.L.
- 309
4
votes
2 answers
Algorithm to find equivalent nodes in isomorphic graphs
Suppose you are given two graphs with $v$ vertices and wish to check whether they are isomorphic are not. One possible way to do this is to enumerate all possible permutations of the $v$ vertices and see if any of these permutations create a…
QC_QAOA
- 12,277