Related papers: The Intersection Problem for Finite Semigroups
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
We study mapping class group orbits of homotopy and isotopy classes of curves with self-intersections. We exhibit the asymptotics of the number of such orbits of curves with a bounded number of self-intersections, as the complexity of the…
The covering number of a nontrivial finite group $G$, denoted $\sigma(G)$, is the smallest number of proper subgroups of $G$ whose set-theoretic union equals $G$. In this article, we focus on a dual problem to that of covering numbers of…
Much use has been made of the techniques of supersymmetric quantum mechanics (SUSY QM) for studying bound-state problems characterized by a superpotential $\phi(x)$. Under the analytic continuation $\phi(x) \to i\phi(x)$, a pair of…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Let X be a coherent configuration associated with a transitive group G. In terms of the intersection numbers of X, a necessary condition for the point stabilizer of G to be a TI-subgroup, is established. Furthermore, under this condition, X…
We study classes of proper restriction semigroups determined by properties of partial actions underlying them. These properties include strongness, antistrongness, being defined by a homomorphism, being an action etc. Of particular interest…
Very little is known about the structure of the intersection of two $k$-generated monoids of words, even for $k=3$. Here we investigate the case of $k$-maximal monoids, that is, monoids whose basis of cardinality $k$ cannot be non-trivially…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem…
This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be strengthened slightly…
In part I we reduced the arithmetic (characteristic zero) version of the P \not \subseteq NP conjecture to the problem of showing that a variety associated with the complexity class NP cannot be embedded in the variety associated the…
We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach---weaker in strength of evidence but more broadly applicable---to suggesting that concrete~NP…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
Fix a finite semigroup $S$ and let $a_1, \ldots, a_k, b$ be tuples in a direct power $S^n$. The subpower membership problem (SMP) for $S$ asks whether $b$ can be generated by $a_1, \ldots, a_k$. For combinatorial Rees matrix semigroups we…
When decomposing a finite semigroup into a wreath product of groups and aperiodic semigroups, complexity measures the minimal number of groups that are needed. Determining an algorithm to compute complexity has been an open problem for…