In this paper we investigate total correctness (termination and correctness simultaneously) in Nonstandard Dynamic Logic (NDL). Here we show that despite of the celebrated Kfoury-Park [5] result, termination is a first order notion if approached properly (e.g. via NDL). In Definition 1 below we recall the famous Manna-Cooper Q-method for proving total correctness. Then we do the same things to ...

In traditional Chinese medicine (TCM), purgation is indicated when a person suffers an illness due to the accumulation of evil internal heat. Obese individuals with a large belly, red face, thick and yellow tongue fur, constipation, and avoidance of heat are thought accumulates of evil internal heat, and they are also treated with purgatives such as Ta-Cheng-Chi-Tang (TCCT), Xiao-Chen-Chi-Tang ...

Sandpile models with conserved number of particles (also called fixed energy sandpiles) may undergo phase transitions between active and absorbing states. We generalize the Manna sandpile model with fixed number of particles, introducing a parameter −1≤ λ≤ 1 related to the toppling of particles from active sites to its first neighbors. In particular, we discuss a model with height restrictions,...

The conserved Manna model with a planar absorbing boundary is studied in various space dimensions. We present a heuristic argument that allows one to compute the surface critical exponent in one dimension analytically. Moreover, we discuss the mean field limit that is expected to be valid in d > 4 space dimensions and demonstrate how the corresponding partial differential equations can be solve...

ion and Modular Veri cation of In nite-State Reactive Systems ? Zohar Manna, Michael A. Col on, Bernd Finkbeiner, Henny B. Sipma and Tom as E. Uribe Computer Science Department Stanford University Stanford, CA. 94305-9045 [email protected] Abstract. We review a number of temporal veri cation techniques for reactive systems using modularity and abstraction. Their use allows the veri cation o...

We study relaxation of long-wavelength density perturbations in a one-dimensional conserved Manna sandpile. Far from criticality where correlation length $\ensuremath{\xi}$ is finite, profiles having wave numbers $k\ensuremath{\rightarrow}0$ diffusive, with time ${\ensuremath{\tau}}_{R}\ensuremath{\sim}{k}^{\ensuremath{-}2}/D$ $D$ being the density-dependent bulk-diffusion coefficient. Near $k\...