2,005 research outputs found
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
A Basic Result on the Theory of Subresultants
Given the polynomials f, g ∈ Z[x] the main result of our paper,
Theorem 1, establishes a direct one-to-one correspondence between the
modified Euclidean and Euclidean polynomial remainder sequences (prs’s) of f, g
computed in Q[x], on one hand, and the subresultant prs of f, g computed
by determinant evaluations in Z[x], on the other.
An important consequence of our theorem is that the signs of Euclidean
and modified Euclidean prs’s - computed either in Q[x] or in Z[x] -
are uniquely determined by the corresponding signs of the subresultant prs’s.
In this respect, all prs’s are uniquely "signed".
Our result fills a gap in the theory of subresultant prs’s. In order to place
Theorem 1 into its correct historical perspective we present a brief historical
review of the subject and hint at certain aspects that need - according to
our opinion - to be revised.
ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2
Fundamentals of Partial Rejection Sampling
Partial Rejection Sampling is an algorithmic approach to obtaining a perfect
sample from a specified distribution. The objects to be sampled are assumed to
be represented by a number of random variables. In contrast to classical
rejection sampling, in which all variables are resampled until a feasible
solution is found, partial rejection sampling aims at greater efficiency by
resampling only a subset of variables that `go wrong'. Partial rejection
sampling is closely related to Moser and Tardos' algorithmic version of the
Lov\'asz Local Lemma, but with the additional requirement that a specified
output distribution should be met. This article provides a largely
self-contained account of the basic form of the algorithm and its analysis
Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]
In this paper we present two new methods for computing the
subresultant polynomial remainder sequence (prs) of two polynomials f, g ∈ Z[x].
We are now able to also correctly compute the Euclidean and modified
Euclidean prs of f, g by using either of the functions employed by our
methods to compute the remainder polynomials.
Another innovation is that we are able to obtain subresultant prs’s in
Z[x] by employing the function rem(f, g, x) to compute the remainder
polynomials in [x]. This is achieved by our method subresultants_amv_q
(f, g, x), which is somewhat slow due to the inherent higher cost of com-
putations in the field of rationals.
To improve in speed, our second method, subresultants_amv(f, g,
x), computes the remainder polynomials in the ring Z[x] by employing the
function rem_z(f, g, x); the time complexity and performance of this
method are very competitive.
Our methods are two different implementations of Theorem 1 (Section 3),
which establishes a one-to-one correspondence between the Euclidean and
modified Euclidean prs of f, g, on one hand, and the subresultant prs of f, g,
on the other.
By contrast, if – as is currently the practice – the remainder polynomi-
als are obtained by the pseudo-remainders function prem(f, g, x) 3 , then
only subresultant prs’s are correctly computed. Euclidean and modified Eu-
clidean prs’s generated by this function may cause confusion with the signs
and conflict with Theorem 1.
ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2
Structural Estimation and Solution of International Trade Models with Heterogeneous Firms
We present an empirical implementation of a general-equilibrium model of international trade with heterogeneous manufacturing firms. The theory underlying our model is consistent with Melitz (2003). A nonlinear structural estimation procedure identifies a set of core parameters and unobserved firm-level trade frictions that best fit the geographic pattern of trade. Once the parameters are identified, we utilize a decomposition technique for computing general-equilibrium counterfactuals. We first assess the economic effects of reductions in measured tariffs. Taking the simple-average welfare change across regions the Melitz structure indicates welfare gains from liberalization that are nearly four times larger than in a standard trade policy simulation. Furthermore, when we compare the economic impact of tariff reductions with reductions in estimated fixed trade costs we find that policy measures affecting the fixed costs are of greater importance than tariff barriers
General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
We construct a Lagrangian description of irreducible integer higher-spin
representations of the Poincare group with an arbitrary Young tableaux having k
rows, on a basis of the universal BRST approach. Starting with a description of
bosonic mixed-symmetry higher-spin fields in a flat space of any dimension in
terms of an auxiliary Fock space associated with special Poincare module, we
realize a conversion of the initial operator constraint system (constructed
with respect to the relations extracting irreducible Poincare-group
representations) into a first-class constraint system. For this purpose, we
find, for the first time, auxiliary representations of the constraint
subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and
containing the subsystem of second-class constraints in terms of new oscillator
variables. We propose a universal procedure of constructing unconstrained
gauge-invariant Lagrangians with reducible gauge symmetries describing the
dynamics of both massless and massive bosonic fields of any spin. It is shown
that the space of BRST cohomologies with a vanishing ghost number is determined
only by the constraints corresponding to an irreducible Poincare-group
representation. As examples of the general procedure, we formulate the method
of Lagrangian construction for bosonic fields subject to arbitrary Young
tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model
of massless rank-4 tensor field with spin and second-stage reducible
gauge symmetries.Comment: 54 pages, abstract, Introduction and Conclusion extended by notes on
new obtained example of Lagrangian for 4-th rank tensor of spin (2,1,1),
Section 6 "Examples" and Appendix D adde
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