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We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
Recently, a new paradigm was introduced in automata theory. The main idea is to classify regular languages according to their propensity to be sorted, establishing a deep connection between automata theory and data compression [J. ACM…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical.…
Given a partially-ordered finite alphabet $\Sigma$ and a language $L\subseteq \Sigma^*$, how large can an antichain in $L$ be (where $L$ is given the lexicographic ordering)? More precisely, since $L$ will in general be infinite, we should…
In the Intersection Non-Emptiness problem, we are given a list of finite automata $A_1,A_2,\dots,A_m$ over a common alphabet $\Sigma$ as input, and the goal is to determine whether some string $w\in \Sigma^*$ lies in the intersection of the…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
A regular language is $k$-piecewise testable if it is a finite boolean combination of languages of the form $\Sigma^* a_1 \Sigma^* \cdots \Sigma^* a_n \Sigma^*$, where $a_i\in\Sigma$ and $0\le n \le k$. Given a DFA $A$ and $k\ge 0$, it is…
The infimal prefix-closed, controllable and observable superlanguage plays an essential role in the relationship between controllability, observability and co-observability -- the central notions of supervisory control theory. Existing…
Given a non-deterministic finite automaton (NFA) A with m states, and a natural number n (presented in unary), the #NFA problem asks to determine the size of the set L(A_n) of words of length n accepted by A. While the corresponding…
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…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
We investigate the constrained synchronization problem for weakly acyclic, or partially ordered, input automata. We show that, for input automata of this type, the problem is always in NP. Furthermore, we give a full classification of the…
We examine the NFA minimization problem in terms of atomic NFA's, that is, NFA's in which the right language of every state is a union of atoms, where the atoms of a regular language are non-empty intersections of complemented and…
Given a regular language L over an ordered alphabet $\Sigma$, the set of lexicographically smallest (resp., largest) words of each length is itself regular. Moreover, there exists an unambiguous finite-state transducer that, on a given word…
Timed languages contain sequences of discrete events ("letters'') separated by real-valued delays, they can be recognized by timed automata, and represent behaviors of various real-time systems. The notion of bandwidth of a timed language…