771 research outputs found
Rational stochastic languages
The goal of the present paper is to provide a systematic and comprehensive
study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A
rational stochastic language is a probability distribution over a free monoid
\Sigma^* which is rational over K, that is which can be generated by a
multiplicity automata with parameters in K. We study the relations between the
classes of rational stochastic languages S rat K (\Sigma). We define the notion
of residual of a stochastic language and we use it to investigate properties of
several subclasses of rational stochastic languages. Lastly, we study the
representation of rational stochastic languages by means of multiplicity
automata.Comment: 35 page
Enumeration of the Monomials of a Polynomial and Related Complexity Classes
We study the problem of generating monomials of a polynomial in the context
of enumeration complexity. In this setting, the complexity measure is the delay
between two solutions and the total time. We present two new algorithms for
restricted classes of polynomials, which have a good delay and the same global
running time as the classical ones. Moreover they are simple to describe, use
little evaluation points and one of them is parallelizable. We introduce three
new complexity classes, TotalPP, IncPP and DelayPP, which are probabilistic
counterparts of the most common classes for enumeration problems, hoping that
randomization will be a tool as strong for enumeration as it is for decision.
Our interpolation algorithms proves that a lot of interesting problems are in
these classes like the enumeration of the spanning hypertrees of a 3-uniform
hypergraph.
Finally we give a method to interpolate a degree 2 polynomials with an
acceptable (incremental) delay. We also prove that finding a specified monomial
in a degree 2 polynomial is hard unless RP = NP. It suggests that there is no
algorithm with a delay as good (polynomial) as the one we achieve for
multilinear polynomials
Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach
This paper discusses the passivity of the port-Hamiltonian formulation of a multivariable impedance matching boundary feedback of fractional order, expressed through diffusive representation. It is first shown in the 1D-wave equation case that the impedance matching boundary feedback can be written as a passive feedback on the boundary port variables. In the Euler-Bernoulli case, the impedance matching feedback matrix involves fractional derivatives and integrals. It is shown that the usual diffusive representation of such feedback is not formally a dissipative port-Hamiltonian system, even if from a frequency point of view this feedback proves passive
Solving the Lipkin model using quantum computers with two qubits only with a hybrid quantum-classical technique based on the Generator Coordinate Method
The possibility of using the generator coordinate method (GCM) using hybrid
quantum-classical algorithms with reduced quantum resources is discussed. The
task of preparing the basis states and calculating the various kernels involved
in the GCM is assigned to the quantum computer, while the remaining tasks, such
as finding the eigenvalues of a many-body problem, are delegated to classical
computers for post-processing the generated kernels. This strategy reduces the
quantum resources required to treat a quantum many-body problem. We apply the
method to the Lipkin model. Using the permutation symmetry of the Hamiltonian,
we show that, ultimately, only two qubits is enough to solve the problem
regardless of the particle number. The classical computing post-processing
leading to the full energy spectrum can be made using standard generalized
eigenvalues techniques by diagonalizing the so-called Hill-Wheeler equation. As
an alternative to this technique, we also explored how the quantum state
deflation method can be adapted to the GCM problem. In this method, variational
principles are iteratively designed to access the different excited states with
increasing energies. The methodology proposed here is successfully applied to
the Lipkin model with a minimal size of two qubits for the quantum register.
The performances of the two classical post-processing approaches with respect
to the statistical noise induced by the finite number of measurements and
quantum devices noise are analyzed. Very satisfactory results for the full
energy spectra are obtained once noise correction techniques are employed.Comment: 12 pages, 8 figure
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