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Computable total functions on metric algebras, universal algebraic specifications and dynamical systems
 THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING
, 2005
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Streams, Stream Transformers and Domain Representations
 Prospects for Hardware Foundations, Lecture Notes in Computer Science
, 1998
"... We present a general theory for the computation of stream transformers of the form F: (R B) (T A), where time T and R, and data A and B, are discrete or continuous. We show how methods for representing topological algebras by algebraic domains can be applied to transformations of continuous ..."
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Cited by 3 (3 self)
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We present a general theory for the computation of stream transformers of the form F: (R B) (T A), where time T and R, and data A and B, are discrete or continuous. We show how methods for representing topological algebras by algebraic domains can be applied to transformations of continuous streams. A stream transformer is continuous in the compactopen topology on continuous streams if and only if it has a continuous lifting to a standard algebraic domain representation of such streams. We also examine the important problem of representing discontinuous streams, such as signals T A, where time T is continuous and data A is discrete.
Stability for Effective Algebras
, 2008
"... We give a general method for showing that all numberings of certain effective algebras are recursively equivalent. The method is based on computable approximationlimit pairs. The approximations are elements of a finitely generated subalgebra, and obtained by computable (nondeterministic) selection ..."
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Cited by 1 (1 self)
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We give a general method for showing that all numberings of certain effective algebras are recursively equivalent. The method is based on computable approximationlimit pairs. The approximations are elements of a finitely generated subalgebra, and obtained by computable (nondeterministic) selection. The results are a continuation of the work by Malâ€™cev, who, for example, showed that finitely generated semicomputable algebras are computably stable. In particular, we generalise the result that the recursive reals are computably stable, if the limit operator is assumed to be computable, to spaces constructed by inverse limits.