Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn-Mal’cev-Neumann generalized power series. We then give a corrected characterization, generalizing our earlier description in terms of finite automata in the case where...

Nested-word automata (NWAs) are a language formalism that helps bridge the gap between finite-state automata and pushdown automata. NWAs can express some context-free properties, such as parenthesis matching, yet retain all the desirable closure characteristics of finite-state automata. This paper describes OpenNWA, a C++ library for working with NWAs. The library provides the expected automata...

We investigate the average-case state and transition complexity of deterministic and nondeterministic finite automata, when choosing a finite language of given maximum word length n uniformly at random. The case where all words are of equal length is also taken into account. It is shown that almost all deterministic finite automata accepting finite languages over a binary input alphabet have st...

We show that the termination of Mohri’s algorithm is decidable for polynomially ambiguous weighted finite automata over the tropical semiring which gives a partial answer to a question by Mohri [29]. The proof relies on an improvement of the notion of the twins property and a Burnside type characterization for the finiteness of the set of states produced by Mohri’s algorithm. ∗An extended abstr...

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.

We associate to each variety of algebras of finite signature a function on the positive integers called the equational complexity of the variety. This function is a measure of how much of the equational theory of a variety must be tested to determine whether a finite algebra belongs to the variety. We provide general methods for giving upper and lower bounds on the growth of equational complexi...

The verification of systems with infinite state spaces has attained considerable attention in recent years. In particular, both global and local model checking techniques have been applied to the verification of such systems. However, new symbolic representations like predicate logics and finite automata have only been used in global model checking. In this paper, we therefore propose a techniq...

We study k-regular sequences from a coalgebraic perspective. Building on the observation that the set of streams over a semiring S can be turned into a final coalgebra, we obtain characterizations of kregular sequences in terms of finite weighted automata, finite systems of behavioral differential equations, and recognizable power series. The latter characterization is obtained via an isomorphi...

We prove that the average complexity, for the uniform distribution on complete deterministic automata, of Moore’s state minimization algorithm is O(n log log n), where n is the number of states in the input automata.

We study the state complexity of languages that can be obtained as reversals of regular languages represented by deterministic finite automata. We show that the state complexity of the reversal of a regular language with state complexity n is between logn and 2. We first prove that the upper bound is tight in the ternary case. Then we present binary languages reaching this upper bound on the re...