9,891 research outputs found
An Approach to Regular Separability in Vector Addition Systems
We study the problem of regular separability of languages of vector addition
systems with states (VASS). It asks whether for two given VASS languages K and
L, there exists a regular language R that includes K and is disjoint from L.
While decidability of the problem in full generality remains an open question,
there are several subclasses for which decidability has been shown: It is
decidable for (i) one-dimensional VASS, (ii) VASS coverability languages, (iii)
languages of integer VASS, and (iv) commutative VASS languages. We propose a
general approach to deciding regular separability. We use it to decide regular
separability of an arbitrary VASS language from any language in the classes
(i), (ii), and (iii). This generalizes all previous results, including (iv)
A Characterization for Decidable Separability by Piecewise Testable Languages
The separability problem for word languages of a class by
languages of a class asks, for two given languages and
from , whether there exists a language from that
includes and excludes , that is, and . In this work, we assume some mild closure properties for
and study for which such classes separability by a piecewise
testable language (PTL) is decidable. We characterize these classes in terms of
decidability of (two variants of) an unboundedness problem. From this, we
deduce that separability by PTL is decidable for a number of language classes,
such as the context-free languages and languages of labeled vector addition
systems. Furthermore, it follows that separability by PTL is decidable if and
only if one can compute for any language of the class its downward closure wrt.
the scattered substring ordering (i.e., if the set of scattered substrings of
any language of the class is effectively regular).
The obtained decidability results contrast some undecidability results. In
fact, for all (non-regular) language classes that we present as examples with
decidable separability, it is undecidable whether a given language is a PTL
itself.
Our characterization involves a result of independent interest, which states
that for any kind of languages and , non-separability by PTL is
equivalent to the existence of common patterns in and
Functional Structure and Approximation in Econometrics (book front matter)
This is the front matter from the book, William A. Barnett and Jane Binner (eds.), Functional Structure and Approximation in Econometrics, published in 2004 by Elsevier in its Contributions to Economic Analysis monograph series. The front matter includes the Table of Contents, Volume Introduction, and Section Introductions by Barnett and Binner and the Preface by W. Erwin Diewert. The volume contains a unified collection and discussion of W. A. Barnett's most important published papers on applied and theoretical econometric modelling.consumer demand, production, flexible functional form, functional structure, asymptotics, nonlinearity, systemwide models
Lifted tensors and Hamilton-Jacobi separability
Starting from a bundle E over R, the dual of the first jet bundle, which is a
co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate
manifold for the geometric description of time-dependent Hamiltonian systems.
Based on previous work, we recall properties of the complete lifts of a type
(1,1) tensor R on E to both of these manifolds. We discuss how an interplay
between these lifted tensors leads to the identification of related
distributions on both manifolds. The integrability of these distributions, a
coordinate free condition, is shown to produce exactly Forbat's conditions for
separability of the time-dependent Hamilton-Jacobi equation in appropriate
coordinates
Separable balls around the maximally mixed multipartite quantum states
We show that for an m-partite quantum system, there is a ball of radius
2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable
(unentangled) positive semidefinite matrices. This can be used to derive an
epsilon below which mixtures of epsilon of any density matrix with 1 - epsilon
of the maximally mixed state will be separable. The epsilon thus obtained is
exponentially better (in the number of systems) than existing results. This
gives a number of qubits below which NMR with standard pseudopure-state
preparation techniques can access only unentangled states; with parameters
realistic for current experiments, this is 23 qubits (compared to 13 qubits via
earlier results). A ball of radius 1 is obtained for multipartite states
separable over the reals.Comment: 8 pages, LaTe
The separation problem for regular languages by piecewise testable languages
Separation is a classical problem in mathematics and computer science. It
asks whether, given two sets belonging to some class, it is possible to
separate them by another set of a smaller class. We present and discuss the
separation problem for regular languages. We then give a direct polynomial time
algorithm to check whether two given regular languages are separable by a
piecewise testable language, that is, whether a sentence can
witness that the languages are indeed disjoint. The proof is a reformulation
and a refinement of an algebraic argument already given by Almeida and the
second author
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