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We study the emptiness and $\lambda$-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its…
We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for…
In the field of computational logic, two classes of finite automata are considered fundamental: deterministic and nondeterministic automata (DFAs and NFAs). In a more fine-grained approach three natural intermediate classes were introduced,…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state…
The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the…
We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and…
We study extremal and algorithmic questions of subset and careful synchronization in monotonic automata. We show that several synchronization problems that are hard in general automata can be solved in polynomial time in monotonic automata,…
Let $\Lambda^{\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\Lambda^{\ast}$, where it extends the divisibility ordering of…
The definition of period in finite-state Markov chains can be extended to regular languages by considering the transitions of DFAs accepting them. For example, the language $(\Sigma\Sigma)^*$ has period two because the length of a recursion…
It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…
This paper investigates the conditions under which a given circular (synchronizing) DFA is \emph{simple} (sometimes referred to as \emph{primitive}) and when it is \emph{irreducible}. Our notion of irreducibility slightly differs from the…
One-way quantum finite automata together with classical states (1QFAC) proposed in [Journal of Computer and System Sciences 81(2) (2015) 359--375] is a new one-way quantum finite automata (1QFA) model that integrates quantum finite automata…
The problem DFA-Intersection-Nonemptiness asks if a given number of deterministic automata accept a common word. In general, this problem is PSPACE-complete. Here, we investigate this problem for the subclasses of commutative automata and…
We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.
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 deterministic finite automaton (DFA) is composite if its language can be decomposed into an intersection of languages of smaller DFAs. Otherwise, A is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
Given a monoid $(M,\varepsilon,\cdot )$ it is shown that a subset $A\subseteq M$ is recognizable in the sense of automata theory if and only if the $\varphi $-rank of $x=x$ is zero in the first-order theory $\operatorname{Th}(M,\varepsilon…