6,686 research outputs found
Semigroups Arising From Asynchronous Automata
We introduce a new class of semigroups arising from a restricted class of
asynchronous automata. We call these semigroups "expanding automaton
semigroups." We show that the class of synchronous automaton semigroups is
strictly contained in the class of expanding automaton semigroups, and that the
class of expanding automaton semigroups is strictly contained in the class of
asynchronous automaton semigroups. We investigate the dynamics of expanding
automaton semigroups acting on regular rooted trees, and show that
undecidability arises in these actions. We show that this class is not closed
under taking normal ideal extensions, but the class of asynchronous automaton
semigroups is closed under taking these extensions. We construct every free
partially commutative monoid as a synchronous automaton semigroup.Comment: 31 pages, 4 figure
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Polynomial Synthesis of Asynchronous Automata
Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be
implemented as a system of synchronized processes with a distributed control
structure called asynchronous automaton. This paper gives a polynomial
algorithm for the synthesis of a non-deterministic asynchronous automaton from
a regular Mazurkiewicz trace language. This new construction is based on an
unfolding approach that improves the complexity of Zielonka's and Pighizzini's
techniques in terms of the number of states.Comment: The MOdelling and VErification (MOVE) tea
On the Control of Asynchronous Automata
The decidability of the distributed version of the Ramadge and Wonham
controller synthesis problem,where both the plant and the controllers are
modeled as asynchronous automataand the controllers have causal memoryis a
challenging open problem.There exist three classes of plants for which the
existence of a correct controller with causal memory has been shown decidable:
when the dependency graph of actions is series-parallel, when the processes are
connectedly communicating and when the dependency graph of processes is a tree.
We design a class of plants, called decomposable games, with a decidable
controller synthesis problem.This provides a unified proof of the three
existing decidability results as well as new examples of decidable plants
Consensus using Asynchronous Failure Detectors
The FLP result shows that crash-tolerant consensus is impossible to solve in
asynchronous systems, and several solutions have been proposed for
crash-tolerant consensus under alternative (stronger) models. One popular
approach is to augment the asynchronous system with appropriate failure
detectors, which provide (potentially unreliable) information about process
crashes in the system, to circumvent the FLP impossibility.
In this paper, we demonstrate the exact mechanism by which (sufficiently
powerful) asynchronous failure detectors enable solving crash-tolerant
consensus. Our approach, which borrows arguments from the FLP impossibility
proof and the famous result from CHT, which shows that is a weakest
failure detector to solve consensus, also yields a natural proof to as
a weakest asynchronous failure detector to solve consensus. The use of I/O
automata theory in our approach enables us to model execution in a more
detailed fashion than CHT and also addresses the latent assumptions and
assertions in the original result in CHT
Asynchronous Games over Tree Architectures
We consider the task of controlling in a distributed way a Zielonka
asynchronous automaton. Every process of a controller has access to its causal
past to determine the next set of actions it proposes to play. An action can be
played only if every process controlling this action proposes to play it. We
consider reachability objectives: every process should reach its set of final
states. We show that this control problem is decidable for tree architectures,
where every process can communicate with its parent, its children, and with the
environment. The complexity of our algorithm is l-fold exponential with l being
the height of the tree representing the architecture. We show that this is
unavoidable by showing that even for three processes the problem is
EXPTIME-complete, and that it is non-elementary in general
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