810 research outputs found
Stable finiteness of ample groupoid algebras, traces and applications
In this paper we study stable finiteness of ample groupoid algebras with
applications to inverse semigroup algebras and Leavitt path algebras,
recovering old results and proving some new ones. In addition, we develop a
theory of (faithful) traces on ample groupoid algebras, mimicking the
-algebra theory but taking advantage of the fact that our functions are
simple and so do not have integrability issues, even in the non-Hausdorff
setting. The theory of traces is closely connected with the theory of invariant
means on Boolean inverse semigroups. We include an appendix on stable
finiteness of more general semigroup algebras, improving on an earlier result
of Munn, which is independent of the rest of the paper
Free L\'evy Processes on Dual Groups
We give a short introduction to the theory of L\'evy processes on dual
groups. As examples we consider L\'evy processes with additive increments and
L\'evy processes on the dual affine group.Comment: 12 pages, Extended abstract to be published in Mini-proceedings:
Second MaPhySto Conference on ``L\'evy Processes - Theory and Applications,''
January 2002, Aarhus, Denmar
Envelopes of conditional probabilities extending a strategy and a prior probability
Any strategy and prior probability together are a coherent conditional
probability that can be extended, generally not in a unique way, to a full
conditional probability. The corresponding class of extensions is studied and a
closed form expression for its envelopes is provided. Then a topological
characterization of the subclasses of extensions satisfying the further
properties of full disintegrability and full strong conglomerability is given
and their envelopes are studied.Comment: 2
Towards the Formal Specification and Verification of Maple Programs
In this paper, we present our ongoing work and initial results on the formal
specification and verification of MiniMaple (a substantial subset of Maple with
slight extensions) programs. The main goal of our work is to find behavioral
errors in such programs w.r.t. their specifications by static analysis. This
task is more complex for widely used computer algebra languages like Maple as
these are fundamentally different from classical languages: they support
non-standard types of objects such as symbols, unevaluated expressions and
polynomials and require abstract computer algebraic concepts and objects such
as rings and orderings etc. As a starting point we have defined and formalized
a syntax, semantics, type system and specification language for MiniMaple
Categorial L\'evy Processes
We generalize Franz' independence in tensor categories with inclusions from
two morphisms (which represent generalized random variables) to arbitrary
ordered families of morphisms. We will see that this only works consistently if
the unit object is an initial object, in which case the inclusions can be
defined starting from the tensor category alone. The obtained independence for
morphisms is called categorial independence. We define categorial L\'evy
processes on every tensor category with initial unit object and present a
construction generalizing the reconstruction of a L\'evy process from its
convolution semigroup via the Daniell-Kolmogorov theorem. Finally, we discuss
examples showing that many known independences from algebra as well as from
(noncommutative) probability are special cases of categorial independence.Comment: Changes in v2: Abstract and introduction extended. Background on
tensor functors moved to Section 2. Example section extended and reorganized.
References updated. Acknowledgements updated. (Some Enrivonment numbers have
changed!
On the Complexity and Performance of Parsing with Derivatives
Current algorithms for context-free parsing inflict a trade-off between ease
of understanding, ease of implementation, theoretical complexity, and practical
performance. No algorithm achieves all of these properties simultaneously.
Might et al. (2011) introduced parsing with derivatives, which handles
arbitrary context-free grammars while being both easy to understand and simple
to implement. Despite much initial enthusiasm and a multitude of independent
implementations, its worst-case complexity has never been proven to be better
than exponential. In fact, high-level arguments claiming it is fundamentally
exponential have been advanced and even accepted as part of the folklore.
Performance ended up being sluggish in practice, and this sluggishness was
taken as informal evidence of exponentiality.
In this paper, we reexamine the performance of parsing with derivatives. We
have discovered that it is not exponential but, in fact, cubic. Moreover,
simple (though perhaps not obvious) modifications to the implementation by
Might et al. (2011) lead to an implementation that is not only easy to
understand but also highly performant in practice.Comment: 13 pages; 12 figures; implementation at
http://bitbucket.org/ucombinator/parsing-with-derivatives/ ; published in
PLDI '16, Proceedings of the 37th ACM SIGPLAN Conference on Programming
Language Design and Implementation, June 13 - 17, 2016, Santa Barbara, CA,
US
On Hoare-McCarthy algebras
We discuss an algebraic approach to propositional logic with side effects. To
this end, we use Hoare's conditional [1985], which is a ternary connective
comparable to if-then-else. Starting from McCarthy's notion of sequential
evaluation [1963] we discuss a number of valuation congruences and we introduce
Hoare-McCarthy algebras as the structures that characterize these congruences.Comment: 29 pages, 1 tabl
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