Related papers: On the Gap Between Separating Words and Separating…
A word $w$ is called a reaching word of a subset $S$ of states in a deterministic finite automaton (DFA) if $S$ is the image of $Q$ under the action of $w$. A DFA is called completely reachable if every non-empty subset of the state set has…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and…
Br\"uggemann-Klein and Wood define a one-unambiguous regular language as a language that can be recognized by a deterministic Glushkov automaton. They give a procedure performed on the minimal DFA, the BW-test, to decide whether a language…
We present a language $L_n$ which is recognizable by a probabilistic finite automaton (PFA) with probability $1 - \epsilon$ for all $\epsilon > 0$ with $O(log^2n)$ states, with a deterministic finite automaton (DFA) with O(n) states, but a…
Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the…
Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…
The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of…
In this paper, we study $w$-frameproof codes, which are equivalent to $\{1,w\}$-separating hash families. Our main results concern binary codes, which are defined over an alphabet of two symbols. For all $w \geq 3$, and for $w+1 \leq N \leq…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
In this note we provide a (decidable) graph-structural characterisation of the infiniteness of $L(w_1, ..., w_k)$, where $L(w_1, ..., w_k) = \{w \in A^* | |w|_{w_1} = \cdots = |w|_{w_k}\}$ is the set of all words that contain the same…
In this note we study automata recognizing birecurrent sets. A set of words is birecurrent if the minimal partial DFA recognizing this set and the minimal partial DFA recognizing the reversal of this set are both strongly connected. This…
This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…
We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…
We propose DFAMiner, a passive learning tool for learning minimal separating deterministic finite automata (DFA) from a set of labelled samples. Separating automata are an interesting class of automata that occurs generally in regular model…
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…
The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language,…
Here we propose an extension of the (deterministic and the nondeterministic) finite automaton with translucent letters (DFAwtl and NFAwtl), which lies between these automata and their non-returning variants (that is, the nr-DFAwtl and the…