Related papers: Large Aperiodic Semigroups
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
For a finite alphabet $\mathcal{A}$ and shift $X\subseteq\mathcal{A}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${\rm Aut}(X)$. For such systems, we…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
This is the first paper in a series of three where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Our main goal is to show that group actions on Z^n-trees give one a powerful tool to…
We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Neural machine translation (NMT) models are typically trained with fixed-size input and output vocabularies, which creates an important bottleneck on their accuracy and generalization capability. As a solution, various studies proposed…
We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular…
What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…
Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…
We discuss the group theory relevant to the ground-state baryons in large N_c QCD. For very large representation, the group generators become classical variables. We find the form of the classical generators for the completely symmetric N…
A word in a free group is called ``potentially positive'' if it is automorphic to an element which is written with only positive exponents. We will develop automata to analyze properties of potentially positive words. We will use these to…
Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{T}_{n}$ be the semigroup of full transformations on $[n]$. Let $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: (for ~all~x,y\in…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…