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Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
A deterministic finite automaton is directable if it has a directing word which takes the automaton from every state to the same state. These notions have been extended also to other kinds of automata. Thus, B.~Imreh and M.~Steinby (1999)…
We consider infinite-state Attacker-Defender games with reachability objectives. The results of the paper are twofold. Firstly we prove a new language-theoretic result for weighted automata on infinite words and show its encoding into the…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and…
Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the n-th level of the hierarchy is over an…
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous…
Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the…
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…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial…
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 introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
A word w of letters on edges of underlying graph Gamma of deterministic finite automaton (DFA) is called the synchronizing word if w sends all states of the automaton to a unique state. J. Cerny discovered in 1964 a sequence of n-state…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by…