268,121 research outputs found
A review of Costas arrays
Costas arrays are not only useful in radar engineering, but they
also present many interesting, and still open, mathematical
problems. This work collects in it all important knowledge about
them available today: some history of the subjects, density
results, construction methods, construction algorithms with full
proofs, and open questions. At the same time all the necessary
mathematical background is offered in the simplest possible format
and terms, so that this work can play the role of a reference for
mathematicians and mathematically inclined engineers interested in the field
Mace4 Reference Manual and Guide
Mace4 is a program that searches for finite models of first-order formulas.
For a given domain size, all instances of the formulas over the domain are
constructed. The result is a set of ground clauses with equality. Then, a
decision procedure based on ground equational rewriting is applied. If
satisfiability is detected, one or more models are printed. Mace4 is a useful
complement to first-order theorem provers, with the prover searching for proofs
and Mace4 looking for countermodels, and it is useful for work on finite
algebras. Mace4 performs better on equational problems than did our previous
model-searching program Mace2.Comment: 17 page
Credible Autocoding of Convex Optimization Algorithms
The efficiency of modern optimization methods, coupled with increasing
computational resources, has led to the possibility of real-time optimization
algorithms acting in safety critical roles. There is a considerable body of
mathematical proofs on on-line optimization programs which can be leveraged to
assist in the development and verification of their implementation. In this
paper, we demonstrate how theoretical proofs of real-time optimization
algorithms can be used to describe functional properties at the level of the
code, thereby making it accessible for the formal methods community. The
running example used in this paper is a generic semi-definite programming (SDP)
solver. Semi-definite programs can encode a wide variety of optimization
problems and can be solved in polynomial time at a given accuracy. We describe
a top-to-down approach that transforms a high-level analysis of the algorithm
into useful code annotations. We formulate some general remarks about how such
a task can be incorporated into a convex programming autocoder. We then take a
first step towards the automatic verification of the optimization program by
identifying key issues to be adressed in future work
Linear perturbations for the vacuum axisymmetric Einstein equations
In axial symmetry, there is a gauge for Einstein equations such that the
total mass of the spacetime can be written as a conserved, positive definite,
integral on the spacelike slices. This property is expected to play an
important role in the global evolution. In this gauge the equations reduce to a
coupled hyperbolic-elliptic system which is formally singular at the axis. Due
to the rather peculiar properties of the system, the local in time existence
has proved to resist analysis by standard methods. To analyze the principal
part of the equations, which may represent the main source of the difficulties,
we study linear perturbation around the flat Minkowski solution in this gauge.
In this article we solve this linearized system explicitly in terms of integral
transformations in a remarkable simple form. This representation is well suited
to obtain useful estimates to apply in the non-linear case.Comment: 13 pages. We suppressed the statements about decay at infinity. The
proofs of these statements were incomplete. The complete proofs will require
extensive technical analysis. We will studied this in a subsequent work. We
also have rewritten the introduction and slighted changed the titl
LIPIcs
Proofs of space (PoS) [Dziembowski et al., CRYPTO'15] are proof systems where a prover can convince a verifier that he "wastes" disk space. PoS were introduced as a more ecological and economical replacement for proofs of work which are currently used to secure blockchains like Bitcoin. In this work we investigate extensions of PoS which allow the prover to embed useful data into the dedicated space, which later can be recovered. Our first contribution is a security proof for the original PoS from CRYPTO'15 in the random oracle model (the original proof only applied to a restricted class of adversaries which can store a subset of the data an honest prover would store). When this PoS is instantiated with recent constructions of maximally depth robust graphs, our proof implies basically optimal security. As a second contribution we show three different extensions of this PoS where useful data can be embedded into the space required by the prover. Our security proof for the PoS extends (non-trivially) to these constructions. We discuss how some of these variants can be used as proofs of catalytic space (PoCS), a notion we put forward in this work, and which basically is a PoS where most of the space required by the prover can be used to backup useful data. Finally we discuss how one of the extensions is a candidate construction for a proof of replication (PoR), a proof system recently suggested in the Filecoin whitepaper
- ā¦