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 of automata on infinite words are necessary for handling real and integer linear arithmetic. This allows the use of substantially simpler algorithms, which have been successfully implemented.

Theoret. Comput. Sci., Vol. 183, No. 1, pp. 93 – 112. This flaw causes subsequent ones

We analyze the minimization problem for deterministic weak automata, a subclass of deterministic Büchi automata, which recognize the regular languages that are recognizable by deterministic Büchi and deterministic co-Büchi automata. We reduce the problem to the minimization of finite automata on finite words and obtain an algorithm running in time O(n log n), where n is the number of states of the automaton.

The paper investigates fixed points and attractors of infinite iterated function systems in Cantor space. By means of the theory of formal languages simple examples of the non-coincidence of fixed point and attractor (closure of the fixed point) are given.

Abstract. We determine completely the Borel hierarchy of the class of context free ω-languages, showing that, for each recursive non null ordinal α, there exist some Σ 0 α-complete and some Π 0 α-complete ω-languages accepted by Büchi 1-counter automata.

We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in constructively given subsets of the Cantor space. Finally, we compare the Kolmogorov complexity to the subword complexity of infinite strings.

We show that many classical decision problems about 1-counter ω-languages, context free ω-languages, or infinitary rational relations, are Π 1 2-complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all Π 1 2-complete for context-free ω-languages or for infinitary rational relations. Topological and arithmetical properties of 1-counter ω-languages, context free ω-languages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1-counter automata or 2-tape automata.

We show how protocols can be derived from norms using landmarks. The resulting protocols can be used by agents to fulfill the norms governing an e-institution without having to have a capability for normative reasoning. It can also be used by normative agents as a default protocol to be used, but from which it can deviate in specific circumstances.

Finite automata are used for the encoding and compression of images. For black-and-white images, for instance, using the quad-tree representation, the black points correspond to ω-words defining the corresponding paths in the tree that lead to them. If the ω-language consisting of the set of all these words is accepted by a deterministic finite automaton then the image is said to be encodable as a finite automaton. For grey-level images and colour images similar representations by automata are in use. In this paper we address the question of which images can be encoded as finite automata with full infinite precision. In applications, of course, the image would be given and rendered at some finite resolution – this amounts to considering a set of finite prefixes of the ω-language – and the features in the image would be approximations of the features in the infinite precision rendering. We focus on the case of black-and-white images – geometrical figures, to be precise – but treat this case in a d-dimensional setting, where d is any

Following Jürgensen and Thierrin [21] we say that an infinite sequence is disjunctive if it contains any (finite) word, or, equivalently, if any word appears in the sequence infinitely many times. "Disjunctivity" is a natural qualitative property; it is weaker, than the property of "normality" (introduced by Borel [1]; see, for instance, Kuipers, Niederreiter [24]). The aim of this paper is to survey some basic results on disjunctive sequences and to explore their role in various areas of mathematics (e.g. in automata-theoretic studies of #-languages or number theory). To achieve our goal we will use various instruments borrowed from topology, measure-theory, probability theory, number theory, automata and formal languages.