51,686 research outputs found
Model-Checking of Ordered Multi-Pushdown Automata
We address the verification problem of ordered multi-pushdown automata: A
multi-stack extension of pushdown automata that comes with a constraint on
stack transitions such that a pop can only be performed on the first non-empty
stack. First, we show that the emptiness problem for ordered multi-pushdown
automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown
automata, the set of all predecessors of a regular set of configurations is an
effectively constructible regular set. We exploit this result to solve the
global model-checking which consists in computing the set of all configurations
of an ordered multi-pushdown automaton that satisfy a given w-regular property
(expressible in linear-time temporal logics or the linear-time \mu-calculus).
As an immediate consequence, we obtain an 2ETIME upper bound for the
model-checking problem of w-regular properties for ordered multi-pushdown
automata (matching its lower-bound).Comment: 31 page
Topology Inspired Problems for Cellular Automata, and a Counterexample in Topology
We consider two relatively natural topologizations of the set of all cellular
automata on a fixed alphabet. The first turns out to be rather pathological, in
that the countable space becomes neither first-countable nor sequential. Also,
reversible automata form a closed set, while surjective ones are dense. The
second topology, which is induced by a metric, is studied in more detail.
Continuity of composition (under certain restrictions) and inversion, as well
as closedness of the set of surjective automata, are proved, and some
counterexamples are given. We then generalize this space, in the sense that
every shift-invariant measure on the configuration space induces a pseudometric
on cellular automata, and study the properties of these spaces. We also
characterize the pseudometric spaces using the Besicovitch distance, and show a
connection to the first (pathological) space.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Revisiting the Rice Theorem of Cellular Automata
A cellular automaton is a parallel synchronous computing model, which
consists in a juxtaposition of finite automata whose state evolves according to
that of their neighbors. It induces a dynamical system on the set of
configurations, i.e. the infinite sequences of cell states. The limit set of
the cellular automaton is the set of configurations which can be reached
arbitrarily late in the evolution.
In this paper, we prove that all properties of limit sets of cellular
automata with binary-state cells are undecidable, except surjectivity. This is
a refinement of the classical "Rice Theorem" that Kari proved on cellular
automata with arbitrary state sets.Comment: 12 pages conference STACS'1
Zenoness for Timed Pushdown Automata
Timed pushdown automata are pushdown automata extended with a finite set of
real-valued clocks. Additionaly, each symbol in the stack is equipped with a
value representing its age. The enabledness of a transition may depend on the
values of the clocks and the age of the topmost symbol. Therefore, dense-timed
pushdown automata subsume both pushdown automata and timed automata. We have
previously shown that the reachability problem for this model is decidable. In
this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
A split-and-perturb decomposition of number-conserving cellular automata
This paper concerns -dimensional cellular automata with the von Neumann
neighborhood that conserve the sum of the states of all their cells. These
automata, called number-conserving or density-conserving cellular automata, are
of particular interest to mathematicians, computer scientists and physicists,
as they can serve as models of physical phenomena obeying some conservation
law. We propose a new approach to study such cellular automata that works in
any dimension and for any set of states . Essentially, the local rule of
a cellular automaton is decomposed into two parts: a split function and a
perturbation. This decomposition is unique and, moreover, the set of all
possible split functions has a very simple structure, while the set of all
perturbations forms a linear space and is therefore very easy to describe in
terms of its basis. We show how this approach allows to find all
number-conserving cellular automata in many cases of and . In
particular, we find all three-dimensional number-conserving CAs with three
states, which until now was beyond the capabilities of computers
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