3,602 research outputs found
Homotopy Bisimilarity for Higher-Dimensional Automata
We introduce a new category of higher-dimensional automata in which the
morphisms are functional homotopy simulations, i.e. functional simulations up
to concurrency of independent events. For this, we use unfoldings of
higher-dimensional automata into higher-dimensional trees. Using a notion of
open maps in this category, we define homotopy bisimilarity. We show that
homotopy bisimilarity is equivalent to a straight-forward generalization of
standard bisimilarity to higher dimensions, and that it is finer than split
bisimilarity and incomparable with history-preserving bisimilarity.Comment: Heavily revised version of arXiv:1209.492
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
Modularizing and Specifying Protocols among Threads
We identify three problems with current techniques for implementing protocols
among threads, which complicate and impair the scalability of multicore
software development: implementing synchronization, implementing coordination,
and modularizing protocols. To mend these deficiencies, we argue for the use of
domain-specific languages (DSL) based on existing models of concurrency. To
demonstrate the feasibility of this proposal, we explain how to use the model
of concurrency Reo as a high-level protocol DSL, which offers appropriate
abstractions and a natural separation of protocols and computations. We
describe a Reo-to-Java compiler and illustrate its use through examples.Comment: In Proceedings PLACES 2012, arXiv:1302.579
Higher Dimensional Transition Systems
We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures
Trace Spaces: an Efficient New Technique for State-Space Reduction
State-space reduction techniques, used primarily in model-checkers, all rely
on the idea that some actions are independent, hence could be taken in any
(respective) order while put in parallel, without changing the semantics. It is
thus not necessary to consider all execution paths in the interleaving
semantics of a concurrent program, but rather some equivalence classes. The
purpose of this paper is to describe a new algorithm to compute such
equivalence classes, and a representative per class, which is based on ideas
originating in algebraic topology. We introduce a geometric semantics of
concurrent languages, where programs are interpreted as directed topological
spaces, and study its properties in order to devise an algorithm for computing
dihomotopy classes of execution paths. In particular, our algorithm is able to
compute a control-flow graph for concurrent programs, possibly containing
loops, which is "as reduced as possible" in the sense that it generates traces
modulo equivalence. A preliminary implementation was achieved, showing
promising results towards efficient methods to analyze concurrent programs,
with very promising results compared to partial-order reduction techniques
Distributed Computation as Hierarchy
This paper presents a new distributed computational model of distributed
systems called the phase web that extends V. Pratt's orthocurrence relation
from 1986. The model uses mutual-exclusion to express sequence, and a new kind
of hierarchy to replace event sequences, posets, and pomsets. The model
explicitly connects computation to a discrete Clifford algebra that is in turn
extended into homology and co-homology, wherein the recursive nature of objects
and boundaries becomes apparent and itself subject to hierarchical recursion.
Topsy, a programming environment embodying the phase web, is available from
www.cs.auc.dk/topsy.Comment: 16 pages, 3 figure
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