Generalizing Computability Theory to Abstract Algebras

DOI10.1007/978-3-319-22156-4_5zbMath1403.03077OpenAlexW2398319463MaRDI QIDQ4637219

J. V. Tucker, Jeffery Zucker

Publication date: 18 April 2018

Published in: Turing’s Revolution (Search for Journal in Brave)

Full work available at URL: https://cronfa.swan.ac.uk/Record/cronfa30876/Download/0030876-31102016101607.pdf

zbMATH Keywords

generalized computabilitycomputability on the realscomputability and continuitycomputability on abstract structuresgeneralized Church-Turing thesis

Mathematics Subject Classification ID

Computation over the reals, computable analysis (03D78) Abstract and axiomatic computability and recursion theory (03D75)

Cites Work

• Characterizations of semicomputable sets of real numbers
• Continuity of operators on continuous and discrete time streams
• Computability of analog networks
• Unifying computers and dynamical systems using the theory of synchronous concurrent algorithms
• Computation by `While' programs on topological partial algebras
• Topological properties of real number representations.
• Computable total functions on metric algebras, universal algebraic specifications and dynamical systems
• Models of computation for partial functions on the reals
• Turing’s Revolution
• Effective procedures in field theory
• Finite alogorithmic procedures and computation theories.
• COMPLEXITY AND REAL COMPUTATION: A MANIFESTO
• Computability of Operators on Continuous and Discrete Time Streams
• Notions of semicomputability in topological algebras over the reals
• Abstract versus concrete computation on metric partial algebras
• Computable Algebra, General Theory and Theory of Computable Fields
• On Computable Numbers, with an Application to the Entscheidungsproblem
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