Questions tagged [computational-complexity]

This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.

355 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
1k views

Computational complexity of topological K-theory

I am a novice with K-theory trying to understand what is and what is not possible. Given a finite simplicial complex $X$, there of course elementary ways to quickly compute the cohomology of $X$ with ...
1k views

2k views

How can an approach to $P$ vs $NP$ based on descriptive complexity avoid being a natural proof in the sense of Raborov-Rudich?

EDIT: This question has been modified to make it a stand-alone question. Feel free to retract your votes for the previous version. Here are Vinay Deolalikar's paper, and Richard Lipton's first post ...
171 views

224 views

Is there an efficient algorithm for testing isomorphism of projective planes?

Isomorphism testing is a core problem in computational complexity. Recently, Babai has shown that Graph Isomorphism problem for general graphs can be solved in quasipolynomial time. Long time before ...
175 views

Is there a Ladner's Theorem" for the PH-vs-PSPACE scenario?

Like a statement of the kind, If the Polynomial Hierarchy (PH) $\neq$ PSPACE then there exists $L \in PSPACE \backslash PH$ which is not PSPACE-complete"? Or is there something else that states ...
2k views

Weighted Hamming distance

Basically my question is, what kind of geometry do we get if we use a "weighted" Hamming distance. This is combinatorics but similar things come up sometimes in theoretical computer science, ...
214 views

Size of 3-SAT assignments

Let $F(N,M)$ be the set of 3-SAT formula with $N$ variables and $M$ clauses. For a given formula $f\in F(N,M)$, we can ask for the set $s_f$ of truth assignments that satisfy $f$. (If $f$ is ...
451 views

Inverse polynomial map $\mathbb{Z}^2\to\mathbb{Z}^2$ growing faster than $2^{2^n}$

Let $P, Q\in \mathbb{Z}[x, y]$ be polynomials with zero constant terms. Assume the induced map $\phi_{P, Q}:\mathbb{Z}^2\to\mathbb{Z}^2$ is injective. An example is $P=x+x^3 y^2, Q=y+x^2 y^3$. Can the ...
77 views

Is recognizing if a Latin square is isotopic to its transpose more efficient than computing its symmetry group?

Ihrig and Ihrig (2007) described a mathematical method for determining if a Latin square is isotopic to its transpose (where isotopic Latin squares vary by permuting the rows, columns and symbols). ...
209 views

Is Hankelability NP-hard?

This question was previously asked on cstheory but with no answers or substantive comments. I am trying to write code to detect if a matrix is a permutation of a Hankel matrix. Here is the spec. ...
191 views

Ricocheting pinball-like shot: Complexity?

Suppose one has $n$ perfect two-sided mirror segments in the plane $\mathbb{R}^2$. The segments are open, excluding their endpoints. They are disjoint as closed segments, i.e., no pair shares an ...
241 views

Recognizing sequences sortable by transpositions?

While reading the post, Probability of generating a desired permutation by random swaps, by Aaronson, and to continue my program I started in this post, How hard is reconstructing a permutation from ...
138 views

Can the isomorphism relation for countable models become harder when adding finitely many constants?

I am particularly interesting in the case where $T$ is o-minimal, but I would be interested in any theory $T$ (or even an $L_{\omega_1,\omega}$-sentence) which has this property. Context: view the ...
703 views

Is the dominating set problem restricted to planar bipartite graphs of maximum degree 3 NP-complete?

Does anyone know about an NP-completeness result for the DOMINATING SET problem in graphs, restricted to the class of planar bipartite graphs of maximum degree 3? I know it is NP-complete for the ...
112 views

Upper bound on the number of perfect matchings in $K_{3,3}$-free graphs

Let $G=(V,E)$ be a graph with an even number of vertices $|V|=2n$. Assume that $G$ is $K_{3,3}$-free i.e. it does not contain a graph isomorphic to biclique $K_{3,3}$. A perfect matching of $G$ is a ...
349 views

Zero-knowledge proofs for answers to the $P=NP$ question

Are there zero-knowledge proofs for every answer to the $P=NP$ question? For instance, if you have a polynomial-time algorithm of moderate complexity for the graph-coloring problem, then it is easy to ...
769 views

Exactly Counting the Number of Lattice Points in an $n$-Dimensional Sphere

Let $S_n(R)$ denote the number of lattice points in an $n$-dimensional "sphere" with radius $R$. For clarification, I am interested in lattice points found both strictly inside the sphere, and on its ...
112 views

Does the problem of recognizing 3DORG-graphs have polynomial complexity?

A 2DORG is the intersection graph of a finite family of rays directed $\to$ or $\uparrow$ in the plane. Such graphs can be recognized effectively (Felsner et al.). A 3DORG is the intersection graph of ...
323 views

Surprising mathematical consequences of of $\mathbf{P} = \mathbf{NP}$

I got interested in the mathematical consequences of $P = NP$ after reading this post, Any important consequences with presupposition of P≠NP . Wang conjectured that if a finite set of Wang tiles ...
268 views

239 views

When is a reduction not a reduction?

Every mathematician understands the concept of reducing a complicated problem to a simpler problem. "Without loss of generality, we may assume…" However, I've noticed that some kinds of "...
278 views

Feasible Type Theories

I am looking for references about efficient type theories, efficiency in the sense of computational complexity, and type theory in the sense of Martin-Lof's type theories. Has there been any studies ...
What is the computational complexity of multiplication in a Carnot group ? Background: A Carnot group is a real nilpotent Lie group $N$ whose Lie algebra $Lie(N)$ admits a direct sum decomposition ...