102,455 research outputs found
Generic process algebra: a programming challenge
Emerging interaction paradigms, such as service-oriented computing, and new technological challenges, such as exogenous component coordination, suggest new roles and application areas for process algebras. This, however, entails the need for more generic and adaptable approaches to their design. For example, some applications may require similar programming constructs coexisting with different interaction disciplines. In such a context, this paper pursues a research programme on a coinductive rephrasal of classic process algebra, proposing a clear separation between structural aspects and interaction disciplines. A particular emphasis is put on the study of interruption combinators defined by natural co-recursion. The paper also illustrates the verification of their properties in an equational and pointfree reasoning style as well as their direct encoding in HaskellFundação para a Ciência e a Tecnologia (FCT
Flat connections and Brauer Type Algebras
We introduce a Brauer type algebra associated with every
pseudo reflection group and every Coxeter group . When is a Coxeter
group of simply-laced type we show is isomorphic to the
generalized Brauer algebra of simply-laced type introduced by Cohen, Gijsbers
and Wales ({\it J. Algebra}, {\bf 280} (2005), 107-153). We also prove has a cellular structure and be semisimple for generic parameters
when is a dihedral group or the type Coxeter group. Moreover, in the
process of construction, we introduce a further generalization of
Lawrence-Krammer representation to complex braid groups associated with all
pseudo reflection groups.Comment: This paper is an improved version of my last one "Algebras associated
with Pseudo Reflection Groups: A Generalization of Brauer Algebras", with
many mistakes corrected and new contents adde
Non-abelian Gerbes and Enhanced Leibniz Algebras
We present the most general gauge-invariant action functional for coupled 1-
and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping
eventual contributions that can be added in particular space-time dimensions
only such as higher Chern-Simons terms. After appropriate field redefinitions
it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the
process one sees explicitly how the existence of a gauge invariant functional
enforces that the most general semi-strict Lie 2-algebra describing the bundle
of a non-abelian gerbe gets reduced to a very particular structure, which,
after the field redefinition, can be identified with the one of an enhanced
Leibniz algebra. This is the first step towards a systematic construction of
such functionals for higher gauge theories, with kinetic terms for a tower of
gauge fields up to some highest form degree p, solved here for p = 2.Comment: Accepted for Publication in Rapid Communications PRD, submitted
originally on April 8, final revised version on June 3
Energy correlations for a random matrix model of disordered bosons
Linearizing the Heisenberg equations of motion around the ground state of an
interacting quantum many-body system, one gets a time-evolution generator in
the positive cone of a real symplectic Lie algebra. The presence of disorder in
the physical system determines a probability measure with support on this cone.
The present paper analyzes a discrete family of such measures of exponential
type, and does so in an attempt to capture, by a simple random matrix model,
some generic statistical features of the characteristic frequencies of
disordered bosonic quasi-particle systems. The level correlation functions of
the said measures are shown to be those of a determinantal process, and the
kernel of the process is expressed as a sum of bi-orthogonal polynomials. While
the correlations in the bulk scaling limit are in accord with sine-kernel or
GUE universality, at the low-frequency end of the spectrum an unusual type of
scaling behavior is found.Comment: 20 pages, 3 figures, references adde
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
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Representation theory of algebras related to the partition algebra
The main objective of this thesis is to determine the complex generic representation theory of the Juyumaya algebra. We do this by showing that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by Martin (the representation theory of which is computable by a combination of classical and category theoretic techniques). We then use this result and general arguments of Cline, Parshall and Scott to prove that the Juyumaya algebra En(x) over the complex field is generically semisimple for all n 2 N. The theoretical background which will facilitate an understanding of the construction process is developed in suitable detail. We also review a result of Martin on the representation theory of the small ramified partition algebra, and fill in some gaps in the proof of this result by providing proofs to results leading to it
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