235 research outputs found
Quantum stochastic convolution cocycles III
Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is
shown to be equivalent to one governed by a quantum stochastic differential
equation, and the generating functionals of norm-continuous convolution
semigroups on a multiplier C*-bialgebra are then completely characterised.
These results are achieved by extending the theory of quantum Levy processes on
a compact quantum group, and more generally quantum stochastic convolution
cocycles on a C*-bialgebra, to locally compact quantum groups and multiplier
C*-bialgebras. Strict extension results obtained by Kustermans, together with
automatic strictness properties developed here, are exploited to obtain
existence and uniqueness for coalgebraic quantum stochastic differential
equations in this setting. Then, working in the universal enveloping von
Neumann bialgebra, we characterise the stochastic generators of Markov-regular,
*-homomorphic (respectively completely positive and contractive), quantum
stochastic convolution cocycles.Comment: 20 pages; v2 corrects some typos and no longer contains a section on
quantum random walk approximations, which will now appear as a separate
submission. The article will appear in the Mathematische Annale
A Backward Analysis for Constraint Logic Programs
One recurring problem in program development is that of understanding how to
re-use code developed by a third party. In the context of (constraint) logic
programming, part of this problem reduces to figuring out how to query a
program. If the logic program does not come with any documentation, then the
programmer is forced to either experiment with queries in an ad hoc fashion or
trace the control-flow of the program (backward) to infer the modes in which a
predicate must be called so as to avoid an instantiation error. This paper
presents an abstract interpretation scheme that automates the latter technique.
The analysis presented in this paper can infer moding properties which if
satisfied by the initial query, come with the guarantee that the program and
query can never generate any moding or instantiation errors. Other applications
of the analysis are discussed. The paper explains how abstract domains with
certain computational properties (they condense) can be used to trace
control-flow backward (right-to-left) to infer useful properties of initial
queries. A correctness argument is presented and an implementation is reported.Comment: 32 page
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