4,311 research outputs found
Between quantum logic and concurrency
We start from two closure operators defined on the elements of a special kind
of partially ordered sets, called causal nets. Causal nets are used to model
histories of concurrent processes, recording occurrences of local states and of
events. If every maximal chain (line) of such a partially ordered set meets
every maximal antichain (cut), then the two closure operators coincide, and
generate a complete orthomodular lattice. In this paper we recall that, for any
closed set in this lattice, every line meets either it or its orthocomplement
in the lattice, and show that to any line, a two-valued state on the lattice
can be associated. Starting from this result, we delineate a logical language
whose formulas are interpreted over closed sets of a causal net, where every
line induces an assignment of truth values to formulas. The resulting logic is
non-classical; we show that maximal antichains in a causal net are associated
to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842
SICStus MT - A Multithreaded Execution Environment for SICStus Prolog
The development of intelligent software agents and other
complex applications which continuously interact with their
environments has been one of the reasons why explicit concurrency has
become a necessity in a modern Prolog system today. Such applications
need to perform several tasks which may be very different with respect
to how they are implemented in Prolog. Performing these tasks
simultaneously is very tedious without language support.
This paper describes the design, implementation and evaluation of a
prototype multithreaded execution environment for SICStus Prolog. The
threads are dynamically managed using a small and compact set of
Prolog primitives implemented in a portable way, requiring almost no
support from the underlying operating system
Fast Quantum Modular Exponentiation
We present a detailed analysis of the impact on modular exponentiation of
architectural features and possible concurrent gate execution. Various
arithmetic algorithms are evaluated for execution time, potential concurrency,
and space tradeoffs. We find that, to exponentiate an n-bit number, for storage
space 100n (twenty times the minimum 5n), we can execute modular exponentiation
two hundred to seven hundred times faster than optimized versions of the basic
algorithms, depending on architecture, for n=128. Addition on a neighbor-only
architecture is limited to O(n) time when non-neighbor architectures can reach
O(log n), demonstrating that physical characteristics of a computing device
have an important impact on both real-world running time and asymptotic
behavior. Our results will help guide experimental implementations of quantum
algorithms and devices.Comment: to appear in PRA 71(5); RevTeX, 12 pages, 12 figures; v2 revision is
substantial, with new algorithmic variants, much shorter and clearer text,
and revised equation formattin
Stochastic Relational Presheaves and Dynamic Logic for Contextuality
Presheaf models provide a formulation of labelled transition systems that is
useful for, among other things, modelling concurrent computation. This paper
aims to extend such models further to represent stochastic dynamics such as
shown in quantum systems. After reviewing what presheaf models represent and
what certain operations on them mean in terms of notions such as internal and
external choices, composition of systems, and so on, I will show how to extend
those models and ideas by combining them with ideas from other
category-theoretic approaches to relational models and to stochastic processes.
It turns out that my extension yields a transitional formulation of
sheaf-theoretic structures that Abramsky and Brandenburger proposed to
characterize non-locality and contextuality. An alternative characterization of
contextuality will then be given in terms of a dynamic modal logic of the
models I put forward.Comment: In Proceedings QPL 2014, arXiv:1412.810
Reachability and Termination Analysis of Concurrent Quantum Programs
We introduce a Markov chain model of concurrent quantum programs. This model
is a quantum generalization of Hart, Sharir and Pnueli's probabilistic
concurrent programs. Some characterizations of the reachable space, uniformly
repeatedly reachable space and termination of a concurrent quantum program are
derived by the analysis of their mathematical structures. Based on these
characterizations, algorithms for computing the reachable space and uniformly
repeatedly reachable space and for deciding the termination are given.Comment: Accepted by Concur'12. Comments are welcom
Big Toy Models: Representing Physical Systems As Chu Spaces
We pursue a model-oriented rather than axiomatic approach to the foundations
of Quantum Mechanics, with the idea that new models can often suggest new
axioms. This approach has often been fruitful in Logic and Theoretical Computer
Science. Rather than seeking to construct a simplified toy model, we aim for a
`big toy model', in which both quantum and classical systems can be faithfully
represented - as well as, possibly, more exotic kinds of systems.
To this end, we show how Chu spaces can be used to represent physical systems
of various kinds. In particular, we show how quantum systems can be represented
as Chu spaces over the unit interval in such a way that the Chu morphisms
correspond exactly to the physically meaningful symmetries of the systems - the
unitaries and antiunitaries. In this way we obtain a full and faithful functor
from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also
consider whether it is possible to use a finite value set rather than the unit
interval; we show that three values suffice, while the two standard
possibilistic reductions to two values both fail to preserve fullness.Comment: 24 pages. Accepted for Synthese 16th April 2010. Published online
20th April 201
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