973 research outputs found
Weak MSO+U with Path Quantifiers over Infinite Trees
This paper shows that over infinite trees, satisfiability is decidable for
weak monadic second-order logic extended by the unbounding quantifier U and
quantification over infinite paths. The proof is by reduction to emptiness for
a certain automaton model, while emptiness for the automaton model is decided
using profinite trees.Comment: version of an ICALP 2014 paper with appendice
Diluted maximum-likelihood algorithm for quantum tomography
We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.Comment: v2: Convergence proof adde
Coherently Controlled Nanoscale Molecular Deposition
Quantum interference effects are shown to provide a means of controlling and
enhancing the focusing a collimated neutral molecular beam onto a surface. The
nature of the aperiodic pattern formed can be altered by varying laser field
characteristics and the system geometry.Comment: 13 pages (inculding 4 figures), LaTeX (Phys. Rev. Lett., 2000, in
Press
Verification of Hierarchical Artifact Systems
Data-driven workflows, of which IBM's Business Artifacts are a prime
exponent, have been successfully deployed in practice, adopted in industrial
standards, and have spawned a rich body of research in academia, focused
primarily on static analysis. The present work represents a significant advance
on the problem of artifact verification, by considering a much richer and more
realistic model than in previous work, incorporating core elements of IBM's
successful Guard-Stage-Milestone model. In particular, the model features task
hierarchy, concurrency, and richer artifact data. It also allows database key
and foreign key dependencies, as well as arithmetic constraints. The results
show decidability of verification and establish its complexity, making use of
novel techniques including a hierarchy of Vector Addition Systems and a variant
of quantifier elimination tailored to our context.Comment: Full version of the accepted PODS pape
Partially Ordered Two-way B\"uchi Automata
We introduce partially ordered two-way B\"uchi automata and characterize
their expressive power in terms of fragments of first-order logic FO[<].
Partially ordered two-way B\"uchi automata are B\"uchi automata which can
change the direction in which the input is processed with the constraint that
whenever a state is left, it is never re-entered again. Nondeterministic
partially ordered two-way B\"uchi automata coincide with the first-order
fragment Sigma2. Our main contribution is that deterministic partially ordered
two-way B\"uchi automata are expressively complete for the first-order fragment
Delta2. As an intermediate step, we show that deterministic partially ordered
two-way B\"uchi automata are effectively closed under Boolean operations.
A small model property yields coNP-completeness of the emptiness problem and
the inclusion problem for deterministic partially ordered two-way B\"uchi
automata.Comment: The results of this paper were presented at CIAA 2010; University of
Stuttgart, Computer Scienc
Packing Returning Secretaries
We study online secretary problems with returns in combinatorial packing
domains with candidates that arrive sequentially over time in random order.
The goal is to accept a feasible packing of candidates of maximum total value.
In the first variant, each candidate arrives exactly twice. All arrivals
occur in random order. We propose a simple 0.5-competitive algorithm that can
be combined with arbitrary approximation algorithms for the packing domain,
even when the total value of candidates is a subadditive function. For
bipartite matching, we obtain an algorithm with competitive ratio at least
for growing , and an algorithm with ratio at least
for all . We extend all algorithms and ratios to arrivals
per candidate.
In the second variant, there is a pool of undecided candidates. In each
round, a random candidate from the pool arrives. Upon arrival a candidate can
be either decided (accept/reject) or postponed (returned into the pool). We
mainly focus on minimizing the expected number of postponements when computing
an optimal solution. An expected number of is always
sufficient. For matroids, we show that the expected number can be reduced to
, where is the minimum of the ranks of matroid and
dual matroid. For bipartite matching, we show a bound of , where
is the size of the optimum matching. For general packing, we show a lower
bound of , even when the size of the optimum is .Comment: 23 pages, 5 figure
Quantum Dynamics of Atom-molecule BECs in a Double-Well Potential
We investigate the dynamics of two-component Bose-Josephson junction composed
of atom-molecule BECs. Within the semiclassical approximation, the multi-degree
of freedom of this system permits chaotic dynamics, which does not occur in
single-component Bose-Josephson junctions. By investigating the level
statistics of the energy spectra using the exact diagonalization method, we
evaluate whether the dynamics of the system is periodic or non-periodic within
the semiclassical approximation. Additionally, we compare the semiclassical and
full-quantum dynamics.Comment: to appear in JLTP - QFS 200
On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases
This article studies the expressive power of finite automata recognizing sets
of real numbers encoded in positional notation. We consider Muller automata as
well as the restricted class of weak deterministic automata, used as symbolic
set representations in actual applications. In previous work, it has been
established that the sets of numbers that are recognizable by weak
deterministic automata in two bases that do not share the same set of prime
factors are exactly those that are definable in the first order additive theory
of real and integer numbers. This result extends Cobham's theorem, which
characterizes the sets of integer numbers that are recognizable by finite
automata in multiple bases.
In this article, we first generalize this result to multiplicatively
independent bases, which brings it closer to the original statement of Cobham's
theorem. Then, we study the sets of reals recognizable by Muller automata in
two bases. We show with a counterexample that, in this setting, Cobham's
theorem does not generalize to multiplicatively independent bases. Finally, we
prove that the sets of reals that are recognizable by Muller automata in two
bases that do not share the same set of prime factors are exactly those
definable in the first order additive theory of real and integer numbers. These
sets are thus also recognizable by weak deterministic automata. This result
leads to a precise characterization of the sets of real numbers that are
recognizable in multiple bases, and provides a theoretical justification to the
use of weak automata as symbolic representations of sets.Comment: 17 page
Базовый алгоритм действия системы поддержки принятия решений
We consider two-player parity games played on transition graphs of higher order pushdown automata. They are ``game-equivalent'' to a kind of model-checking game played on graphs of the infinite hierarchy introduced recently by Caucal. Then in this hierarchy we show how to reduce a game to a graph of lower level. This leads to an effective solution and a construction of the winning strategies
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