Structural Resolution with Co-inductive Loop Detection

A way to combine co-SLD style loop detection with structural resolution was found and is introduced in this work, to extend structural resolution with co-induction. In particular, we present the operational semantics, called co-inductive structural resolution, of this novel combination and prove its soundness with respect to the greatest complete Herbrand model.Comment: In Proceedings CoALP-Ty'16, arXiv:1709.0419

Color-decoupled photo response non-uniformity for digital image forensics

The last few years have seen the use of photo response non-uniformity noise (PRNU), a unique fingerprint of imaging sensors, in various digital forensic applications such as source device identification, content integrity verification and authentication. However, the use of a colour filter array for capturing only one of the three colour components per pixel introduces colour interpolation noise, while the existing methods for extracting PRNU provide no effective means for addressing this issue. Because the artificial colours obtained through the colour interpolation process is not directly acquired from the scene by physical hardware, we expect that the PRNU extracted from the physical components, which are free from interpolation noise, should be more reliable than that from the artificial channels, which carry interpolation noise. Based on this assumption we propose a Couple-Decoupled PRNU (CD-PRNU) extraction method, which first decomposes each colour channel into 4 sub-images and then extracts the PRNU noise from each sub-image. The PRNU noise patterns of the sub-images are then assembled to get the CD-PRNU. This new method can prevent the interpolation noise from propagating into the physical components, thus improving the accuracy of device identification and image content integrity verification

Productive Corecursion in Logic Programming

Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property -- of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no figure

Quantum secure direct communication based on supervised teleportation

We present a quantum secure direct communication(QSDC) scheme as an extension for a proposed supervised secure entanglement sharing protocol. Starting with a quick review on the supervised entanglement sharing protocol -- the "Wuhan" protocol [Y. Li and Y. Liu, arXiv:0709.1449v2], we primarily focus on its further extend using for a QSDC task, in which the communication attendant Alice encodes the secret message directly onto a sequence of 2-level particles which then can be faithfully teleported to Bob using the shared maximal entanglement states obtained by the previous "Wuhan" protocol. We also evaluate the security of the QSDC scheme, where an individual self-attack performed by Alice and Bob -- the out of control attack(OCA) is introduced and the robustness of our scheme on the OCA is documented.Comment: 5 pages, 1 table, oral contribution in the Conference on Quantum Optics and Applications in Computing and Communications, Photonics Asia 2007, Proc. of SPI

Supercritical degenerate parabolic-parabolic Keller-Segel system -- existence criterion given by the best constant in Sobolev's inequality

This article presents a relationship between the sharp constant of the Sobolev inequality and the initial criterion to the global existence of degenerate parabolic-parabolic Keller-Segel system with the diffusion exponent $\frac{2n}{2+n}<m<2-\frac{2}{n}$. The global weak solution obtained in this article does not need any smallness assumption on the initial data. Furthermore, a uniform in time $L^{\infty}$ estimate of the weak solutions is obtained via the Moser iteration, where the constant in $L^p$ estimate for the gradient of the chemical concentration has been exactly formulated in order to complete the iteration process

A note on "Folding wheels and fans."

In S.Gervacio, R.Guerrero and H.Rara, Folding wheels and fans, Graphs and Combinatorics 18 (2002) 731-737, the authors obtain formulas for the clique numbers onto which wheels and fans fold. We present an interpolation theorem which generalizes their theorems 4.2 and 5.2. We show that their formula for wheels is wrong. We show that for threshold graphs, the achromatic number and folding number coincides with the chromatic number

A linear-time algorithm for the strong chromatic index of Halin graphs

We show that there exists a linear-time algorithm that computes the strong chromatic index of Halin graphs.Comment: 7 page