Related papers: Semigroup intersection problems in the Heisenberg …
Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…
We investigate the computational complexity of various decision problems related to conjugacy in finite inverse semigroups. We describe polynomial-time algorithms for checking if two elements in such a semigroup are ~p conjugate and whether…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
We consider two group actions on $m$-tuples of $n \times n$ matrices. The first is simultaneous conjugation by $\operatorname{GL}_n$ and the second is the left-right action of $\operatorname{SL}_n \times \operatorname{SL}_n$. We give…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
We investigate the computational complexity for determining various properties of a finite transformation semigroup given by generators. We introduce a simple framework to describe transformation semigroup properties that are decidable in…
We prove that the inhabitation problem for rank two intersection types is decidable, but (contrary to common belief) EXPTIME-hard. The exponential time hardness is shown by reduction from the in-place acceptance problem for alternating…
We construct group codes over two letters (i.e., bases of subgroups of a two-generated free group) with special properties. Such group codes can be used for reducing algorithmic problems over large alphabets to algorithmic problems over a…
The Orbit Problem consists of determining, given a matrix $A\in \mathbb{R}^{d\times d}$ and vectors $x,y\in \mathbb{R}^d$, whether there exists $n\in \mathbb{N}$ such that $A^n=y$. This problem was shown to be decidable in a seminal work of…
Let ${\mathbf P}$ be the class of polynomial-time decision problems and $\mathbf{NP}$ be the class of nondeterministic polynomial time decision problems. We prove the following: Theorem 3. The classes ${\mathbf P}$ and $\mathbf{NP}$ are…
A semigroup conjugacy is an equivalence relation that equals group conjugacy when the semigroup is a group. In this note, we answer five open problems related to semigroup conjugacy. (Problem One) We say a conjugacy ~ is partition-covering…
For a finite group $G$, let $\omega(G)$ be the set of element orders of $G$ and let $h(G)$ be the number of pairwise nonisomorphic finite groups $H$ with $\omega(H)=\omega(G)$. We say that the recognition problem is solved for $G$ if the…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…
In this paper we study decidability and complexity of decision problems on matrices from the special linear group $\mathrm{SL}(2,\mathbb{Z})$. In particular, we study the freeness problem: given a finite set of matrices $G$ generating a…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We shed some light on the problem of determining the orbits of the braid group action on semiorthonormal bases of Mukai lattices as considered in \cite{GK04} and \cite{GO1}. We show that there is an algebraic (and in particular algorithmic)…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
This work presents a sample constructions of two algebras both with the ideal of relations defined by a finite Gr\"obner basis. For the first algebra the question whether a given element is nilpotent is algorithmically unsolvable, for the…