How likely is that a randomly given (non-) deterministic finite automaton recognizes no word? A quick reflection seems to indicate that not too many finite automata accept no word; but, can this intuition be confirmed? In this paper we offer a statistical approach which allows us to conclude that for automata, with a large enough number of states, the probability that a given (non-) determinist...

In this paper we answer an open question about the exact bound on the maximal number of non-mergible states in nondeterministic finite automaton (NFA). It is shown that the maximal possible number of non-mergible states in a NFA that accepts a given regular language L is not greater than 2n − 1, where n is the number of states in the minimal deterministic finite automaton that accepts L. Next w...

A word is called a reset word for a deterministic finite automaton if it maps all states of the automaton to a unique state. Deciding about the existence of a reset word of a given length for a given automaton is known to be a NP-complete problem. We use tools provided by Bodlaender et al. (2007) to prove that such problem, parameterized by number of states, does not admit a polynomial kernel u...

The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(n) such that: (i) There is a one-way quantum finite automaton (qfa) of O(n) st...

The factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of factors of w. It is a data structure allowing the search of a pattern in a text in time and space proportional to the length of the pattern. In this paper we link classical combinatorial parameters on words to the size and the structure of the factor automaton. As a main result, we give a chara...

Previously, self-verifying symmetric difference automata were defined and a tight bound of 2n−1−1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n≥ 2, there is a regular languageLn accepted by a non-unary self-verifying symmetric difference nondeterministic automaton with n states, such that its equivalent minimal deterministic fini...

We extend the automata-theoretic framework for reasoning about infinitestate sequential systems to handle also the global model-checking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Chec...

We consider systems of finite automata performing together computation on an input string. Each automaton has its own read head that moves independently of the other heads, but the automata cooperate in making state transitions. Computational power of such devices depends on the number of states of automata, the number of automata, and the way they cooperate. We concentrate our attention on the...

A mobile agent (robot), modeled as a finite automaton, has to visit all nodes of a regular graph. How does the memory size of the agent (the number of states of the automaton) influence its exploration capability? In particular, does every increase of the memory size enable an agent to explore more graphs? We give a partial answer to this problem by showing that a strict gain of the exploration...