A sequence w over a finite alphabet A is generated by a uniform automaton if there exists an automaton labelled on {0, . . . , k − 1} for some k > 1 and recognizing for each output a in A the set of positions of a in w expressed in base k. Automatic sequences are generated by finite automata. By considering pushdown automata instead of finite ones, we generate exactly the context-free sequences...

There are several well known algorithms to minimize deterministic finite automata. Apart from the theoretical worst-case running time analysis, however, not much is known about the average-case analysis or practical performance of each of these algorithms. On this paper we compare three minimization algorithms based on experimental results. The choice of the algorithms was based on the fact tha...

Abstract We consider the notion of a constant length queue automaton —i.e., traditional with built-in limit on its queue—as formalism for representing regular languages. show that descriptional power automata greatly outperforms finite state automata, height pushdown and straight line programs expressions, by providing optimal exponential double-exponential size gaps. Moreover, we prove can be ...

This paper studies the expressive power of finite-state automata recognizing sets of real numbers encoded positionally. It is known that the sets that are definable in the first-order additive theory of real and integer variables 〈R, Z,+, <〉 can all be recognized by weak deterministic Büchi automata, regardless of the encoding base r > 1. In this paper, we prove the reciprocal property, i.e., t...

Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the worst-case. To overcome this, simple heuristic methods have been proposed. In this paper we analyse some of the heuristics presented in the literature and propos...

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for ...

Learning automata is a foundational problem in computational learning theory. However, even efficiently learning random DFAs is hard. A natural restriction of this problem is to consider learning random DFAs under the uniform distribution. To date, this problem has no non-trivial lower bounds nor algorithms faster than brute force. In this note, we propose a method to find faster algorithms for...