Related papers: Quasigroup words and reversible automata
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Let $F_n$ be the free group on $n$ generators and $\Gamma_g$ the surface group of genus $g$. We consider two particular generating sets: the set of all primitive elements in $F_n$ and the set of all simple loops in $\Gamma_g$. We give a…
We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and…
In this paper we survey some surprising connections between group theory, the theory of automata and formal languages, the theory of ends, infinite games of perfect information, and monadic second-order logic.
The paper counts the number of reduced quasigroup words of a particular length in a certain number of generators. Taking account of the relationship with the Catalan numbers, counting words in a free magma, we introduce the term…
An {\omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {\omega}-languages, i.e. the class of {\omega}-languages accepted by Turing machines with a B\"uchi acceptance condition, which is…
The $\mathit{\Pi}$ family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic datatypes. In this paper, we give a denotational semantics for this…
This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we…
The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid…
Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words,…
We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and a head carrying a state. These homeomorphisms can only…
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 show that the word problem for an amalgam $[S_1,S_2;U,\omega_1,\omega_2]$ of inverse semigroups may be undecidable even if we assume $S_1$ and $S_2$ (and therefore $U$) to have finite $\mathcal{R}$-classes and $\omega_1,\omega_2$ to be…
We propose and evaluate antichain algorithms to solve the universality and language inclusion problems for nondeterministic Buechi automata, and the emptiness problem for alternating Buechi automata. To obtain those algorithms, we establish…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
The word problem is an old and central problem in (computational) group theory. It is well-known that the word problem is undecidable in general, but decidable for specific types of presentations. Consistent polycyclic presentations are an…
We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…