Domains of Commutative C-Subalgebras

C. Heunen, B. Lindenhovius

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative sub algebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.
Original languageEnglish
Title of host publicationLogic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages450-461
Number of pages12
DOIs
Publication statusPublished - 1 Jul 2015

Keywords

  • algebra
  • approximation theory
  • quantum computing
  • Lawson topology
  • commutative C*-subalgebras
  • deterministic computing
  • domain theory
  • modelling information approximation
  • operator algebras
  • probabilistic computing
  • reversible computing
  • uniform semantics
  • Algebra
  • Approximation methods
  • Computational modeling
  • Probabilistic logic
  • Quantum computing
  • Semantics
  • Topology
  • C-algebra
  • Domain

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