Discounting in LTL

In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of \emph{how well} the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to {\em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions

Modified Three-Step Search Block Matching Motion Estimation and Weighted Finite Automata based Fractal Video Compression

The major challenge with fractal image/video coding technique is that, it requires more encoding time. Therefore, how to reduce the encoding time is the research component remains in the fractal coding. Block matching motion estimation algorithms are used, to reduce the computations performed in the process of encoding. The objective of the proposed work is to develop an approach for video coding using modified three step search (MTSS) block matching algorithm and weighted finite automata (WFA) coding with a specific focus on reducing the encoding time. The MTSS block matching algorithm are used for computing motion vectors between the two frames i.e. displacement of pixels and WFA is used for the coding as it behaves like the Fractal Coding (FC). WFA represents an image (frame or motion compensated prediction error) based on the idea of fractal that the image has self-similarity in itself. The self-similarity is sought from the symmetry of an image, so the encoding algorithm divides an image into multi-levels of quad-tree segmentations and creates an automaton from the sub-images. The proposed MTSS block matching algorithm is based on the combination of rectangular and hexagonal search pattern and compared with the existing New Three-Step Search (NTSS), Three-Step Search (TSS), and Efficient Three-Step Search (ETSS) block matching estimation algorithm. The performance of the proposed MTSS block matching algorithm is evaluated on the basis of performance evaluation parameters i.e. mean absolute difference (MAD) and average search points required per frame. Mean of absolute difference (MAD) distortion function is used as the block distortion measure (BDM). Finally, developed approaches namely, MTSS and WFA, MTSS and FC, and Plane FC (applied on every frame) are compared with each other. The experimentations are carried out on the standard uncompressed video databases, namely, akiyo, bus, mobile, suzie, traffic, football, soccer, ice etc. Developed approaches are compared on the basis of performance evaluation parameters, namely, encoding time, decoding time, compression ratio and Peak Signal to Noise Ratio (PSNR). The video compression using MTSS and WFA coding performs better than MTSS and fractal coding, and frame by frame fractal coding in terms of achieving reduced encoding time and better quality of video