## Chu Spaces: Automata with quantum aspects (1994)

Venue: | In Proc. Workshop on Physics and Computation (PhysComp’94 |

Citations: | 8 - 3 self |

### BibTeX

@INPROCEEDINGS{Pratt94chuspaces:,

author = {Vaughan R. Pratt},

title = {Chu Spaces: Automata with quantum aspects},

booktitle = {In Proc. Workshop on Physics and Computation (PhysComp’94},

year = {1994},

pages = {186--195},

publisher = {IEEE}

}

### OpenURL

### Abstract

Chu spaces are a recently developed model of concurrent computation extending automata theory to express branching time and true concurrency. They exhibit in a primitive form the quantum mechanical phenomena of complementarity and uncertainty. The complementarity arises as the duality of information and time, automata and schedules, and states and events. Uncertainty arises when we define a measurement to be a morphism and notice that increasing structure in the observed object reduces clarity of observation. For a Chu space this uncertainty can be calculated numerically in an attractively simple way directly from its form factor to yield the usual Heisenberg uncertainty relation. Chu spaces correspond to wavefunctions as vectors of Hilbert space, whose inner product operation is realized for Chu spaces as right residuation and whose quantum logic becomes Girard's linear logic. 1 Introduction 1.1 Prospects for Chu Spaces The automaton model of this paper, Chu spaces, is an outgrowth ...

### Citations

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(Show Context)
Citation Context ...ily confined to set theory and number theory. A set is a relational structure with the empty language. Without language such a structure can signify nothing beyond cardinality. Not even quantum logic =-=[BvN36]-=- abstracts that far, retaining the binary relation of orthogonality on an “orthoframe” as the primitive dictionary entry for its Kripke semantics, and the logical connectives of conjunction (interpret... |

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60 |
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Citation Context ...s from the same account at remote automatic teller machines. A succession of models addressed these two issues during the 1980's, initially separately and then later jointly. R. van Glabbeek's thesis =-=[vG90]-=- provides a comprehensive summary of the state of the art in 1990. This paper is based on a model that is, we feel, a particularly clean example of the state of that art. It has two main sources for i... |

55 | Origins of the calculus of binary relations - Pratt - 1992 |

54 |
The logic of quantum mechanics
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(Show Context)
Citation Context ...ily confined to set theory and number theory. A set is a relational structure with the empty language. Without language such a structure can signify nothing beyond cardinality. Not even quantum logic =-=[BvN36] abstracts-=- that far, retaining the binary relation of orthogonality on an "orthoframe" as the primitive dictionary entry for its Kripke semantics, and the logical connectives of conjunction (interpret... |

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(Show Context)
Citation Context ...unts to modus ponens, and makes SnR the corresponding intuitionistic implication, S implies R. The above expression for ! then becomes j= n j=, making it the right residual of j= by itself. Elsewhere =-=[Pra90]-=- we have shown that the equation (RnR) = RnR, namely that RnR is its own reflexive transitive closure (the meaning of * here), amounts to an induction axiom leading to a complete and finite equational... |

50 |
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Citation Context ... the order of occurrence in that string. The new automata theory raised two objections to this conception. The first was raised by Robin Milner in his book on CCS, a Calculus of Communicating Systems =-=[Mil80]-=-. The standard model appears to condense all choices about behavior into a single selection of a string from a language made at the start of the behavior. Real behavior however makes informed decision... |

49 | Chu Spaces: A Model of Concurrency - Gupta - 1994 |

48 |
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(Show Context)
Citation Context ...is not an operator but rather a form of inner product for a generalized vector space V over K, with point set A and dual point set X (the functionals from H to K). As observed by Lafont and Streicher =-=[LS91]-=-, such a Chu space, or game as they call it, is an ordinary vector space just when K is the underlying set of a field k, A is the underlying set of a vector space V over k, and X consists of the funct... |

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16 |
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Citation Context ...ct F (c) transforms in the same way that c does. Concreteness means that c and its representation F (c) have the same underlying set, an essential missing detail of previous such universality results =-=[HL69]-=-. For example groups with carrier (underlying set) G are realized as ternary relational structures on G (whence concreteness) , the ternary relation being xy = z; monoids are quaternary because the un... |

16 | Linear logic for generalized quantum mechanics
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Citation Context ...challenge. 2 In fact even more so, Chu spaces viewed equivalently as either matrices or Boolean propositions being conceptually simpler than ortholattices. discussed at length at the previous meeting =-=[Pra93a]-=-, linear logic resembles quantum logic in some respects while improving on it in others. The resemblances are in details such as rejection of distributivity of conjunction over disjunction and accepta... |

12 |
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Citation Context ...s, we feel, a particularly clean example of the state of that art. It has two main sources for its basic structure, the event spaces of Winskel [NPW81, Win88], and the *-autonomous categories of Barr =-=[Bar79]-=-, originally done entirely independently of any possibility of its application to computer science. More specifically it makes use of those *-autonomous categories arising from a construction studied ... |

8 | Concurrent program schemas and their interpretation - Mazurkiewicz - 1977 |

4 | spaces: Complementarity and uncertainty in rational mechanics - Chu - 1994 |