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An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite,…
Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
A data language is a set of finite words defined on an infinite alphabet. Data languages are used to express properties associated with data values (domain defined over a countably infinite set). In this paper, we introduce set augmented…
The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set…
This paper demonstrates a task to finetune a BART model so it can construct a sentence from an arbitrary set of words, which used to be a difficult NLP task. The training task is making sentences with four words, but the trained model can…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a…
Given a finite set of words w1,...,wn independently drawn according to a fixed unknown distribution law P called a stochastic language, an usual goal in Grammatical Inference is to infer an estimate of P in some class of probabilistic…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…
This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called $\Phi$-dynamical system. Secondly, the strongest…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
Bilingual lexicons form a critical component of various natural language processing applications, including unsupervised and semisupervised machine translation and crosslingual information retrieval. We improve bilingual lexicon induction…
Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…
Natural language generation systems (NLG) map non-linguistic representations into strings of words through a number of steps using intermediate representations of various levels of abstraction. Template based systems, by contrast, tend to…
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown…
It is proved that every regular expression of alphabetic width $n$, that is, with $n$ occurrences of symbols of the alphabet, can be transformed into a deterministic finite automaton (DFA) with $2^{\frac{n}{2}+(\frac{\log_2…
In this paper we investigate finitely generated ideals in the Nevanlinna class. We prove analogues to some known results for the algebra of bounded analytic functions $H^{\infty}$. We also show that, in contrast to the $H^{\infty}$-case,…
We study a fixed-window counting system in which integers are represented by words of constant length while the alphabet grows as needed. This viewpoint arises from De Bruijn sequences: for fixed order $n$, the reverse prefer-max sequence…
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…