725 research outputs found
Relative directed homotopy theory of partially ordered spaces
Algebraic topological methods have been used successfully in concurrency
theory, the domain of theoretical computer science that deals with distributed
computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially
ordered spaces (pospaces) as a model for concurrent systems. In this paper it
is shown that the category of pospaces under a fixed pospace is both a
fibration and a cofibration category in the sense of H. Baues. The homotopy
notion in this fibration and cofibration category is relative directed
homotopy. It is also shown that the category of pospaces is a closed model
category such that the homotopy notion is directed homotopy.Comment: 20 page
Note on L.-S. category and DGA modules
Prova tipográfica (In Press)We define an algebraic approximation of the Lusternik-Schnirelmann category
of a map and show that this invariant lies
between A-category and M-category. We derive from this result a characterization of the Lusternik-Schnirelmann category of a rational space
Estruturas algébricas
Apontamentos das aulas teóricas de Estruturas Algébricas da Licenciatura em Ciências da Computaçã
Weak equivalence of higher-dimensional automata
This paper introduces a notion of equivalence for higher-dimensional
automata, called weak equivalence. Weak equivalence focuses mainly on a
traditional trace language and a new homology language, which captures the
overall independence structure of an HDA. It is shown that weak equivalence is
compatible with both the tensor product and the coproduct of HDAs and that,
under certain conditions, HDAs may be reduced to weakly equivalent smaller ones
by merging and collapsing cubes
On the homology language of HDA models of transition systems
Given a transition system with an independence relation on the alphabet of
labels, one can associate with it a usually very large symmetric
higher-dimensional automaton. The purpose of this paper is to show that by
choosing an acyclic relation whose symmetric closure is the given independence
relation, it is possible to construct a much smaller nonsymmetric HDA with the
same homology language.Comment: 17 page
Some collapsing operations for 2-dimensional precubical sets
In this paper, we consider 2-dimensional precubical sets, which can be used
to model systems of two concurrently executing processes. From the point of
view of concurrency theory, two precubical sets can be considered equivalent if
their geometric realizations have the same directed homotopy type relative to
the extremal elements in the sense of P. Bubenik. We give easily verifiable
conditions under which it is possible to reduce a 2-dimensional precubical set
to an equivalent smaller one by collapsing an edge or eliminating a square and
one or two free faces. We also look at some simple standard examples in order
to illustrate how our results can be used to construct small models of
2-dimensional precubical sets.Comment: New title, completely revised version of "Reducing cubical set models
of concurrent systems
Weak equivalence of higher-dimensional automata
This paper introduces a notion of equivalence for higher-dimensional
automata, called weak equivalence. Weak equivalence focuses mainly on a
traditional trace language and a new homology language, which captures the
overall independence structure of an HDA. It is shown that weak equivalence is
compatible with both the tensor product and the coproduct of HDAs and that,
under certain conditions, HDAs may be reduced to weakly equivalent smaller ones
by merging and collapsing cubes.This research was partially supported by FCT (Fundacao para a Ciencia e a Tecnologia, Portugal) through project UID/MAT/00013/2013
Simplicial resolutions and Ganea fibrations
In this work, we compare the two approximations of a path-connected space
, by the Ganea spaces and by the realizations of the truncated simplicial resolutions emerging from the
loop-suspension cotriple . For a simply connected space , we
construct maps over , up to homotopy. In the case , we prove the existence of
a map over (up to homotopy) and
conjecture that this map exists for any
Joins of DGA modules and sectional category
We construct an explicit semifree model for the fiber join of two fibrations
p: E --> B and p': E' --> B from semifree models of p and p'. Using this model,
we introduce a lower bound of the sectional category of a fibration p which can
be calculated from any Sullivan model of p and which is closer to the sectional
category of p than the classical cohomological lower bound given by the
nilpotency of the kernel of p^*: H^*(B;Q) --> H^*(E;Q). In the special case of
the evaluation fibration X^I --> X x X we obtain a computable lower bound of
Farber's topological complexity TC(X). We show that the difference between this
lower bound and the classical cohomological lower bound can be arbitrarily
large.Comment: This is the version published by Algebraic & Geometric Topology on 24
February 200
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