Abstraction Refinement for Large Scale Model Checking summarizes recent research on abstraction techniques for model checking large digital system. Considering both the size of today's digital systems and the capacity of state-of-the-art verification algorithms, abstraction is the only viable solution for the successful application of model checking techniques to industrial-scale designs. This book describes recent research developments in automatic abstraction refinement techniques. The suite of algorithms presented in this book has demonstrated significant improvement over prior art; some...

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems,...

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory-a unified view of continuous and discrete analysis-has been widely used to...