15 citations · 29 across the 8 of their papers we have counts for
9 papers
Concurrent Gaussian elimination
Ulrich Berger, Monika Seisenberger, Dieter Spreen +1
Working in a semi-constructive logical system that supports the extraction of concurrent programs, we extract a program inverting non-singular real valued matrices from a construct…
How Much Partiality Is Needed for a Theory of Computability?
Dieter Spreen
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termina…
Bi-topological spaces and the Continuity Problem
Dieter Spreen
The \emph{Continuity Problem} is the question whether effective operators are continuous, where an effective operator is a function on a space of constructively given objects $…
Computing with Infinite Objects: the Gray Code Case
Dieter Spreen, Ulrich Berger
Infinite Gray code has been introduced by Tsuiki as a redundancy-free representation of the reals. In applications the signed digit representation is mostly used which has maximal…
Computing with Continuous Objects: A Uniform Co-inductive Approach
Dieter Spreen
A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown…
Information Systems with Witnesses: The Function Space Construction
Dieter Spreen
Information systems with witnesses have been introduced in [D. Spreen. Generalised information systems capture L-domains. arXiv:1610.02260v2] as a logic-style representation of L-d…
Generalised Information Systems Capture L-Domains
Dieter Spreen
A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised…
Some results related to the continuity problem
Dieter Spreen
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 s…
A Coinductive Approach to Computing with Compact Sets
Ulrich Berger, Dieter Spreen
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 a…