108,645 research outputs found
Complexity in Prefix-Free Regular Languages
We examine deterministic and nondeterministic state complexities of regular
operations on prefix-free languages. We strengthen several results by providing
witness languages over smaller alphabets, usually as small as possible. We next
provide the tight bounds on state complexity of symmetric difference, and
deterministic and nondeterministic state complexity of difference and cyclic
shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Cyclic redundancy check-based detection algorithms for automatic identification system signals received by satellite.
This paper addresses the problem of demodulating signals transmitted in the automatic identification system. The main characteristics of such signals consist of two points: (i) they are modulated using a trellis-coded modulation, more precisely a Gaussian minimum shift keying modulation; and (ii) they are submitted to a bit stuffing procedure, which makes more difficult the detection of the transmitted information bits. This paper presents several demodulation algorithms developed in different contexts: mono-user and multi-user transmissions, and known/unknown phase shift. The proposed receiver uses the cyclic redundancy check (CRC) present in the automatic identification system signals for error correction and not for error detection only. By using this CRC, a particular Viterbi algorithm, on the basis of a so-called extended trellis, is developed. This trellis is defined by extended states composed of a trellis code state and a CRC state. Moreover, specific conditional transitions are defined to take into account the possible presence of stuffing bits. The algorithms proposed in the multi-user scenario present a small increase of computation complexity with respect to the mono-user algorithms. Some performance results are presented for several scenarios in the context of the automatic identification system and compared with those of existing techniques developed in similar scenarios
Formal Languages in Dynamical Systems
We treat here the interrelation between formal languages and those dynamical
systems that can be described by cellular automata (CA). There is a well-known
injective map which identifies any CA-invariant subshift with a central formal
language. However, in the special case of a symbolic dynamics, i.e. where the
CA is just the shift map, one gets a stronger result: the identification map
can be extended to a functor between the categories of symbolic dynamics and
formal languages. This functor additionally maps topological conjugacies
between subshifts to empty-string-limited generalized sequential machines
between languages. If the periodic points form a dense set, a case which arises
in a commonly used notion of chaotic dynamics, then an even more natural map to
assign a formal language to a subshift is offered. This map extends to a
functor, too. The Chomsky hierarchy measuring the complexity of formal
languages can be transferred via either of these functors from formal languages
to symbolic dynamics and proves to be a conjugacy invariant there. In this way
it acquires a dynamical meaning. After reviewing some results of the complexity
of CA-invariant subshifts, special attention is given to a new kind of
invariant subshift: the trapped set, which originates from the theory of
chaotic scattering and for which one can study complexity transitions.Comment: 23 pages, LaTe
Study of noise in virtual distillation circuits for quantum error mitigation
Virtual distillation has been proposed as an error mitigation protocol for
estimating the expectation values of observables in quantum algorithms. It
proceeds by creating a cyclic permutation of noisy copies of a quantum
state using a sequence of controlled-swap gates. If the noise does not shift
the dominant eigenvector of the density operator away from the ideal state,
then the error in expectation-value estimation can be exponentially reduced
with . In practice, subsequent error-mitigation techniques are required to
suppress the effect of noise in the cyclic permutation circuit itself, leading
to increased experimental complexity. Here, we perform a careful analysis of
noise in the cyclic permutation circuit and find that the estimation of
expectation value of observables diagonal in the computational basis is robust
against dephasing noise. We support the analytical result with numerical
simulations and find that of errors are reduced for , with physical
dephasing error probabilities as high as . Our results imply that a broad
class of quantum algorithms can be implemented with higher accuracy in the
near-term with qubit platforms where non-dephasing errors are suppressed, such
as superconducting bosonic qubits and Rydberg atoms.Comment: 12 pages, 5 figure
Effective Theories for Circuits and Automata
Abstracting an effective theory from a complicated process is central to the
study of complexity. Even when the underlying mechanisms are understood, or at
least measurable, the presence of dissipation and irreversibility in
biological, computational and social systems makes the problem harder. Here we
demonstrate the construction of effective theories in the presence of both
irreversibility and noise, in a dynamical model with underlying feedback. We
use the Krohn-Rhodes theorem to show how the composition of underlying
mechanisms can lead to innovations in the emergent effective theory. We show
how dissipation and irreversibility fundamentally limit the lifetimes of these
emergent structures, even though, on short timescales, the group properties may
be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure
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