We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. First we compute upper bounds using structural properties of minimal deterministic finite-state automata for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on th...

Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible languages, respectively. The existence of k-reversible languages which are not (k−1)-reversible is known, for each k > 1. This gives an infinite hierarchy o...

We consider the task of exploring graphs with anonymous nodes by a team of non-cooperative robots modeled as finite automata. These robots have no a priori knowledge of the topology of the graph, or of its size. Each edge has to be traversed by at least one robot. We first show that, for any set of q non-cooperative K-state robots, there exists a graph of size O(qK) that no robot of this set ca...

We present an efficient incremental algorithm for learning deterministic finite state automata (DFA) from labeled examples and membership queries. This algorithm is an extension of Angluin’s ID procedure to an incremental framework. The learning algorithm is intermittently provided with labeled examples and has access to a knowledgeable teacher capable of answering membership queries. The learn...

It is shown that the universe problem L(A ) = A is undecidable for 4-state nite automata A with integer weights such that the weights of the paths are unimodal. The language L(A ) is de ned as the set of words w for which there exists a path of A having zero weight, that is, ( ) = 0.

This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this involves some difficult and delicate to implement algorithms. The contribution of this paper is to show, using topological arguments, that only a restricted class...

Checking whether one formal language is included in another is vital to many verification tasks. In this paper, we provide solutions for checking the inclusion of the languages given by visibly pushdown automata over both finite and infinite words. Visibly pushdown automata are a richer automaton model than the classical finite-state automata, which allows one, e.g., to reason about the nesting...

We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale’s linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continui...

The study of descriptional complexity issues for finite automata dates back to the mid 1950’s. One of the earliest results is that deterministic and nondeterministic finite automata are computationally equivalent, and that nondeterministic finite automata can offer exponential state savings compared to deterministic ones, see [11]—by the powerset construction one increases the number of states ...