21,638 research outputs found
Model-Checking the Higher-Dimensional Modal mu-Calculus
The higher-dimensional modal mu-calculus is an extension of the mu-calculus
in which formulas are interpreted in tuples of states of a labeled transition
system. Every property that can be expressed in this logic can be checked in
polynomial time, and conversely every polynomial-time decidable problem that
has a bisimulation-invariant encoding into labeled transition systems can also
be defined in the higher-dimensional modal mu-calculus. We exemplify the latter
connection by giving several examples of decision problems which reduce to
model checking of the higher-dimensional modal mu-calculus for some fixed
formulas. This way generic model checking algorithms for the logic can then be
used via partial evaluation in order to obtain algorithms for theses problems
which may benefit from improvements that are well-established in the field of
program verification, namely on-the-fly and symbolic techniques. The aim of
this work is to extend such techniques to other fields as well, here
exemplarily done for process equivalences, automata theory, parsing, string
problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317
Higher-Dimensional Timed Automata
We introduce a new formalism of higher-dimensional timed automata, based on
van Glabbeek's higher-dimensional automata and Alur's timed automata. We prove
that their reachability is PSPACE-complete and can be decided using zone-based
algorithms. We also show how to use tensor products to combat state-space
explosion and how to extend the setting to higher-dimensional hybrid automata
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
Computing Aggregate Properties of Preimages for 2D Cellular Automata
Computing properties of the set of precursors of a given configuration is a
common problem underlying many important questions about cellular automata.
Unfortunately, such computations quickly become intractable in dimension
greater than one. This paper presents an algorithm --- incremental aggregation
--- that can compute aggregate properties of the set of precursors
exponentially faster than na{\"i}ve approaches. The incremental aggregation
algorithm is demonstrated on two problems from the two-dimensional binary Game
of Life cellular automaton: precursor count distributions and higher-order mean
field theory coefficients. In both cases, incremental aggregation allows us to
obtain new results that were previously beyond reach
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
Investigating The Algebraic Structure of Dihomotopy Types
This presentation is the sequel of a paper published in GETCO'00 proceedings
where a research program to construct an appropriate algebraic setting for the
study of deformations of higher dimensional automata was sketched. This paper
focuses precisely on detailing some of its aspects. The main idea is that the
category of homotopy types can be embedded in a new category of dihomotopy
types, the embedding being realized by the Globe functor. In this latter
category, isomorphism classes of objects are exactly higher dimensional
automata up to deformations leaving invariant their computer scientific
properties as presence or not of deadlocks (or everything similar or related).
Some hints to study the algebraic structure of dihomotopy types are given, in
particular a rule to decide whether a statement/notion concerning dihomotopy
types is or not the lifting of another statement/notion concerning homotopy
types. This rule does not enable to guess what is the lifting of a given
notion/statement, it only enables to make the verification, once the lifting
has been found.Comment: 28 pages ; LaTeX2e + 4 figures ; Expository paper ; Minor typos
corrections ; To appear in GETCO'01 proceeding
Computational Processes and Incompleteness
We introduce a formal definition of Wolfram's notion of computational process
based on cellular automata, a physics-like model of computation. There is a
natural classification of these processes into decidable, intermediate and
complete. It is shown that in the context of standard finite injury priority
arguments one cannot establish the existence of an intermediate computational
process
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