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It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S). The definition of these automata is straightforward as it…
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
A two-dimensional automaton operates on arrays of symbols. While a standard (four-way) two-dimensional automaton can move its input head in four directions, restricted two-dimensional automata are only permitted to move their input heads in…
We investigate the language classes recognized by group automata over matrix groups. We present a summary of the results obtained so far together with a number of new results. We look at the computational power of time-bounded group…
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated meta Hahn algebra and its finite-dimensional representations.…
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…
Finite-state automata are a very effective tool in natural language processing. However, in a variety of applications and especially in speech precessing, it is necessary to consider more general machines in which arcs are assigned weights…
In this article, we study classes of multidimensional subshifts defined by multihead finite automata, in particular the hierarchy of classes of subshifts defined as the number of heads grows. The hierarchy collapses on the third level,…
Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by…
Whereas conventional state-of-the-art image processing systems of recording and output devices almost exclusively utilize square arranged methods, biological models, however, suggest an alternative, evolutionarily-based structure. Inspired…
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…
We introduce presheaf automata as a generalisation of different variants of higher-dimensional automata and other automata-like formalisms, including Petri nets and vector addition systems. We develop the foundations of a language theory…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear…