28,973 research outputs found
Sound and complete axiomatizations of coalgebraic language equivalence
Coalgebras provide a uniform framework to study dynamical systems, including
several types of automata. In this paper, we make use of the coalgebraic view
on systems to investigate, in a uniform way, under which conditions calculi
that are sound and complete with respect to behavioral equivalence can be
extended to a coarser coalgebraic language equivalence, which arises from a
generalised powerset construction that determinises coalgebras. We show that
soundness and completeness are established by proving that expressions modulo
axioms of a calculus form the rational fixpoint of the given type functor. Our
main result is that the rational fixpoint of the functor , where is a
monad describing the branching of the systems (e.g. non-determinism, weights,
probability etc.), has as a quotient the rational fixpoint of the
"determinised" type functor , a lifting of to the category of
-algebras. We apply our framework to the concrete example of weighted
automata, for which we present a new sound and complete calculus for weighted
language equivalence. As a special case, we obtain non-deterministic automata,
where we recover Rabinovich's sound and complete calculus for language
equivalence.Comment: Corrected version of published journal articl
Bi-differential calculi and integrable models
The existence of an infinite set of conserved currents in completely
integrable classical models, including chiral and Toda models as well as the KP
and self-dual Yang-Mills equations, is traced back to a simple construction of
an infinite chain of closed (respectively, covariantly constant) 1-forms in a
(gauged) bi-differential calculus. The latter consists of a differential
algebra on which two differential maps act. In a gauged bi-differential
calculus these maps are extended to flat covariant derivatives.Comment: 24 pages, 2 figures, uses amssymb.sty and diagrams.sty, substantial
extensions of examples (relative to first version
Bi-differential calculus and the KdV equation
A gauged bi-differential calculus over an associative (and not necessarily
commutative) algebra A is an N-graded left A-module with two covariant
derivatives acting on it which, as a consequence of certain (e.g., nonlinear
differential) equations, are flat and anticommute. As a consequence, there is
an iterative construction of generalized conserved currents. We associate a
gauged bi-differential calculus with the Korteweg-de-Vries equation and use it
to compute conserved densities of this equation.Comment: 9 pages, LaTeX, uses amssymb.sty, XXXI Symposium on Mathematical
Physics, Torun, May 1999, replaces "A notion of complete integrability in
noncommutative geometry and the Korteweg-de-Vries equation
Bicomplexes and Integrable Models
We associate bicomplexes with several integrable models in such a way that
conserved currents are obtained by a simple iterative construction. Gauge
transformations and dressings are discussed in this framework and several
examples are presented, including the nonlinear Schrodinger and sine-Gordon
equations, and some discrete models.Comment: 17 pages, LaTeX, uses amssymb.sty and diagrams.st
Taverna Workflows: Syntax and Semantics
This paper presents the formal syntax and the operational semantics of Taverna, a workflow management system with a large user base among the e-Science community. Such formal foundation, which has so far been lacking, opens the way to the translation between Taverna workflows and other process models. In particular, the ability to automatically compile a simple domain-specific process description into Taverna facilitates its adoption by e-scientists who are not expert workflow developers. We demonstrate this potential through a practical use case
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