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## 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 language | English |
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Title of host publication | Logic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on |

Publisher | Institute of Electrical and Electronics Engineers (IEEE) |

Pages | 450-461 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 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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## Projects

- 1 Finished