Dieter Spreen | University of Siegen (original) (raw)

Papers by Dieter Spreen

WORLD SCIENTIFIC eBooks, Apr 1, 2023

arXiv (Cornell University), May 11, 2023

arXiv (Cornell University), Apr 11, 2020

Springer eBooks, 1984

ABSTRACT

A logic-oriented representation of L-domains in the style of Scott’s information sys-

Archive for Mathematical Logic, 2004

From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 Spatial Representation: Discrete vs. Contin... more From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 Spatial Representation: Discrete vs. Continuous Computational Models was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The rst section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Infinite Gray code has been introduced by Tsuiki <cit.> as a redundancy-free representation... more Infinite Gray code has been introduced by Tsuiki <cit.> as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal redundancy. Tsuiki presented a functional program converting signed digit code into infinite Gray code. Moreover, he showed that infinite Gray code can effectively be converted into signed digit code, but the program needs to have some non-deterministic features (see also <cit.>). Berger and Tsuiki <cit.> reproved the result in a system of formal first-order intuitionistic logic extended by inductive and co-inductive definitions, as well as some new logical connectives capturing concurrent behaviour. The programs extracted from the proofs are exactly the ones given by Tsuiki. In order to do so, co-inductive predicates and are defined and the inclusion ⊆ is derived. For the converse inclusion the new logical connectives are used to introduce a concurrent version _2 of S and ⊆_2 is s...

Journal of Information Processing and Cybernetics, 1988

ABSTRACT An important problem in automata theory is the question whether the state equivalence is... more ABSTRACT An important problem in automata theory is the question whether the state equivalence is decidable. For some special types of automata a positive answer has been given to the question. All these results were proved separately. In this paper a uniform approach such that these results can be obtained as special cases is presented. Moreover, from the central result analogous results are derived for some classes of automata for which the decidability of the state equivalence has not yet been considered such as weighted automata, lattice automata, module automata, and linear stochastically independent automata. Furthermore, via this approach known bounds on the length of the input words which have to be considered in order to decide the state equivalence are improved. For Boolean automata the known bound is 2 2 n -1. The bound presented is 2 n -1. It cannot be improved.

Exact representations of real numbers such as the signed digit representation or more generally l... more Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first author it was shown how to extract certified algorithms working with the signed digit representations from constructive proofs. In this paper we lay the foundation for doing a similar thing with nonempty compact sets. It turns out that a representation by streams of finitely many digits is impossible and instead trees are needed.

The continuity problem, i.e., the question whether effective maps between effectively given topol... more The continuity problem, i.e., the question whether effective maps between effectively given topological spaces are effectively continuous, is reconsidered. In earlier work it was shown that this is always the case, if the effective map also has a witness for noninclusion. The extra condition does not have an obvious topological interpretation. As is shown in the present paper, it appears naturally where in the classical proof that sequentially continuous maps are continuous the Axiom of Choice is used. The question is therefore whether the witness condition appears in the general continuity theorem only for this reason, i.e., whether effective operators are effectively sequentially continuous. For two large classes of spaces covering all important applications it is shown that this is indeed the case. The general question, however, remains open. Spaces in this investigation are in general not required to be Hausdorff. They only need to satisfy the weaker T_0 separation condition.

Paris-Diderot, FR, Jean-Eric.Pin@liafa.univ-paris-diderot.fr 3 A. P. Ershov Institute-Novosibirsk... more Paris-Diderot, FR, Jean-Eric.Pin@liafa.univ-paris-diderot.fr 3 A. P. Ershov Institute-Novosibirsk, RU, vseliv@iis.nsk.su 4 Universität Siegen, DE, spreen@math.uni-siegen.de Abstract Duality allows one to move between the two worlds: the world of certain algebras of properties and a spacial world of individuals, thereby leading to a change of perspective that may, and often does, lead to new insights. Dualities have given rise to active research in a number of areas of theoretical computer science. Dagstuhl Seminar 13311 "Duality in Computer Science" was held to stimulate research in this area. This report collects the ideas that were presented and discussed during the course of the seminar. Seminar License Creative Commons BY 3.0 Unported license © Mai Gehrke, Jean-Eric Pin, Victor Selivanov, and Dieter Spreen This seminar concentrated on applications of duality in computation, semantics, and formal languages. Duality and computation Consider the area of exact real number ...

There is a large gap between mathematical structures and the structures computer implementations ... more There is a large gap between mathematical structures and the structures computer implementations are based on. To stimulate research to overcome this-especially for infinitary structures-highly non-trivial problem the Dagstuhl Seminar 11411 "Computing with Infinite Data: Topolo-gical and Logical Foundations" was held. This report collects the ideas that were presented and discussed during the course of the seminar.

Abstract. From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351 Spa-