Properties of Kripke structures can be expressed by formulas of the modal µ-calculus. Despite its strong expressive power, the validity problem of the modal µ-calculus is decidable, and so are some of its variants enriched by inverse programs, graded modalities, and nominals. In this study, we show that the pre- and post-conditions of transformations of Kripke structures, such as addition/deletion of states and edges, can be expressed using variants of the modal µ-calculus. Combined with decision procedures we have developed for those variants, the properties of sequences of transformations on Kripke structures can be deduced. We show that these techniques can be used to verify the properties of pointer-manipulating programs.

Java is one of important program language today. In Java, in order to build sound software, we have to carefully implement two fundamental methods hashCode and equals. This requirement, however, is not easy to follow in real software development. Some existing studies for ensuring the correctness of these two methods rely on static analysis, which are limited to loop-free programs. This paper proposes a new solution to this important problem, using software analysis workbench (SAW), an open source tool. The efficiency is evaluated through experiments. We also provide a useful situation where cost of regression testing is reduced when program refactoring is conducted.

Probabilistic model checking is an emerging technology for analyzing systems which exhibit stochastic behaviors. The verification of a larger system using probabilistic model checking faces the same state explosion problem as ordinary model checking. Probabilistic symmetry reduction is a technique to tackle this problem. In this paper, we study probabilistic symmetry reduction for a system with a ring buffer which can describe various applications. A key of probabilistic symmetry reduction is identifying symmetry of states with respect to the structure of the target system. We introduce two functions; Shiftδ and Reverse to clarify such symmetry. Using these functions, we also present pseudo code to construct a quotient model. Then, we show two practical case studies; the one-dimensional Ising model and the Automatic Identification System (AIS). Behaviors of them were verified, but suffered from the state explosion problem. Through the case studies, we show that probabilistic symmetry reduction takes advantage of reducing the size of state space.

Probabilistic model checking is an emerging verification technology for probabilistic analysis. Its use has been started not only in computer science but also in interdisciplinary fields. In this paper, we show that probabilistic model checking allows one to analyze the magnetic behaviors of the one-dimensional Ising model, which describes physical phenomena of magnets. The Ising model consists of elementary objects called spins and its dynamics is often represented as the Metropolis method. To analyze the Ising model with probabilistic model checking, we build Discrete Time Markov Chain (DTMC) models that represent the behavior of the Ising model. Two representative physical quantities, i.e., energy and magnetization, are focused on. To assess these quantities using model checking, we devise formulas in Probabilistic real time Computation Tree Logic (PCTL) that represent the quantities. To demonstrate the feasibility of the proposed approach, we show the results of an experiment using the PRISM model checker.