671 research outputs found
A Compositional Framework for Preference-Aware Agents
A formal description of a Cyber-Physical system should include a rigorous
specification of the computational and physical components involved, as well as
their interaction. Such a description, thus, lends itself to a compositional
model where every module in the model specifies the behavior of a
(computational or physical) component or the interaction between different
components. We propose a framework based on Soft Constraint Automata that
facilitates the component-wise description of such systems and includes the
tools necessary to compose subsystems in a meaningful way, to yield a
description of the entire system. Most importantly, Soft Constraint Automata
allow the description and composition of components' preferences as well as
environmental constraints in a uniform fashion. We illustrate the utility of
our framework using a detailed description of a patrolling robot, while
highlighting methods of composition as well as possible techniques to employ
them.Comment: In Proceedings V2CPS-16, arXiv:1612.0402
Tensor products and regularity properties of Cuntz semigroups
The Cuntz semigroup of a C*-algebra is an important invariant in the
structure and classification theory of C*-algebras. It captures more
information than K-theory but is often more delicate to handle. We
systematically study the lattice and category theoretic aspects of Cuntz
semigroups.
Given a C*-algebra , its (concrete) Cuntz semigroup is an object
in the category of (abstract) Cuntz semigroups, as introduced by Coward,
Elliott and Ivanescu. To clarify the distinction between concrete and abstract
Cuntz semigroups, we will call the latter -semigroups.
We establish the existence of tensor products in the category and study
the basic properties of this construction. We show that is a symmetric,
monoidal category and relate with for
certain classes of C*-algebras.
As a main tool for our approach we introduce the category of
pre-completed Cuntz semigroups. We show that is a full, reflective
subcategory of . One can then easily deduce properties of from
respective properties of , e.g. the existence of tensor products and
inductive limits. The advantage is that constructions in are much easier
since the objects are purely algebraic.
We also develop a theory of -semirings and their semimodules. The Cuntz
semigroup of a strongly self-absorbing C*-algebra has a natural product giving
it the structure of a -semiring. We give explicit characterizations of
-semimodules over such -semirings. For instance, we show that a
-semigroup tensorially absorbs the -semiring of the Jiang-Su
algebra if and only if is almost unperforated and almost divisible, thus
establishing a semigroup version of the Toms-Winter conjecture.Comment: 195 pages; revised version; several proofs streamlined; some results
corrected, in particular added 5.2.3-5.2.
Soft constraint abstraction based on semiring homomorphism
The semiring-based constraint satisfaction problems (semiring CSPs), proposed
by Bistarelli, Montanari and Rossi \cite{BMR97}, is a very general framework of
soft constraints. In this paper we propose an abstraction scheme for soft
constraints that uses semiring homomorphism. To find optimal solutions of the
concrete problem, the idea is, first working in the abstract problem and
finding its optimal solutions, then using them to solve the concrete problem.
In particular, we show that a mapping preserves optimal solutions if and only
if it is an order-reflecting semiring homomorphism. Moreover, for a semiring
homomorphism and a problem over , if is optimal in
, then there is an optimal solution of such that
has the same value as in .Comment: 18 pages, 1 figur
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