152 research outputs found
Degree of Sequentiality of Weighted Automata
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA.
For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE
-complete
Simulations of Weighted Tree Automata
Simulations of weighted tree automata (wta) are considered. It is shown how
such simulations can be decomposed into simpler functional and dual functional
simulations also called forward and backward simulations. In addition, it is
shown in several cases (fields, commutative rings, Noetherian semirings,
semiring of natural numbers) that all equivalent wta M and N can be joined by a
finite chain of simulations. More precisely, in all mentioned cases there
exists a single wta that simulates both M and N. Those results immediately
yield decidability of equivalence provided that the semiring is finitely (and
effectively) presented.Comment: 17 pages, 2 figure
On the Number of Synchronizing Colorings of Digraphs
We deal with -out-regular directed multigraphs with loops (called simply
\emph{digraphs}). The edges of such a digraph can be colored by elements of
some fixed -element set in such a way that outgoing edges of every vertex
have different colors. Such a coloring corresponds naturally to an automaton.
The road coloring theorem states that every primitive digraph has a
synchronizing coloring.
In the present paper we study how many synchronizing colorings can exist for
a digraph with vertices. We performed an extensive experimental
investigation of digraphs with small number of vertices. This was done by using
our dedicated algorithm exhaustively enumerating all small digraphs. We also
present a series of digraphs whose fraction of synchronizing colorings is equal
to , for every and the number of vertices large enough.
On the basis of our results we state several conjectures and open problems.
In particular, we conjecture that is the smallest possible fraction of
synchronizing colorings, except for a single exceptional example on 6 vertices
for .Comment: CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1
On Functionality of Visibly Pushdown Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that
(strictly) extends finite state transducers with a stack. Like visibly pushdown
automata, the input symbols determine the stack operations. In this paper, we
prove that functionality is decidable in PSpace for visibly pushdown
transducers. The proof is done via a pumping argument: if a word with two
outputs has a sufficiently large nesting depth, there exists a nested word with
two outputs whose nesting depth is strictly smaller. The proof uses technics of
word combinatorics. As a consequence of decidability of functionality, we also
show that equivalence of functional visibly pushdown transducers is
Exptime-Complete.Comment: 20 page
On the Commutative Equivalence of Context-Free Languages
The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated
Effective-field-theory approach to persistent currents
Using an effective-field-theory (nonlinear sigma model) description of
interacting electrons in a disordered metal ring enclosing magnetic flux, we
calculate the moments of the persistent current distribution, in terms of
interacting Goldstone modes (diffusons and cooperons). At the lowest or
Gaussian order we reproduce well-known results for the average current and its
variance that were originally obtained using diagrammatic perturbation theory.
At this level of approximation the current distribution can be shown to be
strictly Gaussian. The nonlinear sigma model provides a systematic way of
calculating higher-order contributions to the current moments. An explicit
calculation for the average current of the first term beyond Gaussian order
shows that it is small compared to the Gaussian result; an order-of-magnitude
estimation indicates that the same is true for all higher-order contributions
to the average current and its variance. We therefore conclude that the
experimentally observed magnitude of persistent currents cannot be explained in
terms of interacting diffusons and cooperons.Comment: 12 pages, no figures, final version as publishe
Angular position of nodes in the superconducting gap of YBCO
The thermal conductivity of a YBCO single crystal has been studied as a
function of the relative orientation of the crystal axes and a magnetic field
rotating in the Cu-O planes. Measurements were carried out at several
temperatures below T_c and at a fixed field of 30 kOe. A four-fold symmetry
characteristic of a superconducting gap with nodes at odd multiples of 45
degrees in k-space was resolved. Experiments were performed to exclude a
possible macroscopic origin for such a four-fold symmetry such as sample shape
or anisotropic pinning. Our results impose an upper limit of 10% on the weight
of the s-wave component of the essentially d-wave superconducting order
parameter of YBCO.Comment: 10 pages, 4 figure
Coupled CDW and SDW Fluctuations as an Origin of Anomalous Properties of Ferromagnetic Superconductor UGe_2
It is shown that anomalous properties of UGe_2 can be understood in a unified
way on the basis of a single assumption that the superconductivity is mediated
by the coupled SDW and CDW fluctuations induced by the imperfect nesting of the
Fermi surface with majority spins at T=T_x(P) deep in the ferromagnetic phase.
Excess growth of uniform magnetization is shown to develop in the temperature
range T<T_x(P) as a mode-coupling effect of coupled growth of SDW and CDW
orderings, which has been observed by two different types of experiments. The
coupled CDW and SDW fluctuations are shown to be essentially ferromagnetic spin
fluctuations which induce a spin-triplet p-wave attraction. These fluctuations
consist of two modes, spin and charge fluctuations with large momentum transfer
of the nesting vector. An anomalous temperature dependence of the upper
critical field H_c2(T) such as crossing of H_c2(T) at P=11.4 kbar and P=13.5
kbar, can be understood by the strong-coupling-superconductivity formalism.
Temperature dependence of the lattice specific heat including a large shoulder
near T_x is also explained quite well as an effect of a kind of Kohn anomaly
associated with coupled SDW-CDW transition.Comment: (12 pages, 10 eps figures) submitted to J. Phys. Soc. Jp
Superconducting gap node spectroscopy using nonlinear electrodynamics
We present a method to determine the nodal structure of the energy gap of
unconventional superconductors such as high materials. We show how
nonlinear electrodynamics phenomena in the Meissner regime, arising from the
presence of lines on the Fermi surface where the superconducting energy gap is
very small or zero, can be used to perform ``node spectroscopy'', that is, as a
sensitive bulk probe to locate the angular position of those lines. In
calculating the nonlinear supercurrent response, we include the effects of
orthorhombic distortion and plane anisotropy. Analytic results presented
demonstrate a systematic way to experimentally distinguish order parameters of
different symmetries, including cases with mixed symmetry (for example,
and ). We consider, as suggested by various experiments, order parameters
with predominantly -wave character, and describe how to determine the
possible presence of other symmetries. The nonlinear magnetic moment displays a
distinct behavior if nodes in the gap are absent but regions with small,
finite, values of the energy gap exist.Comment: 18 pages, Revtex, 9 postscript figures. Submitted to Phys. Rev
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