This paper is concerned with exploring an extended approach for the stability analysis and synthesis for Markovian jump nonlinear systems (MJNLSs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the MJNLSs with incomplete transition description. In this paper, not all the elements of the rate transition matrices (RTMs), or probability transition matrices (PTMs) are assumed to be known. By fully considering the properties of the RTMs and PTMs, sufficient criteria of stability and stabilization is obtained in both continuous and discrete-time. Stabilization conditions with a mode-dependent fuzzy controller are derived for Markovian jump fuzzy systems in terms of linear matrix inequalities (LMIs), which can be readily solved by using existing LMI optimization techniques. Finally, illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

State Transition Matrix (STM) is a table-based modeling language that has been frequently used in industry for specifying behaviors of systems. Functional correctness of a STM design (i.e., a design developed with STM) could often be expressed as invariant properties. In this paper, we first present a formalization of the static and dynamic aspects of STM designs. Consequentially, based on this formalization, we investigate a symbolic encoding approach, through which a STM design could be bounded model checked w.r.t. invariant properties by using Satisfiability Modulo Theories (SMT) solving technique. We have built a prototype implementation of the proposed encoding and the state-of-the-art SMT solver - Yices, is used in our experiments to evaluate the effectiveness of our approach. Two attempts for accelerating SMT solving are also reported.

In this paper, we give a theoretical analysis of χ2 attack proposed by Knudsen and Meier on the RC6 block cipher. To this end, we propose a method of security evaluation against χ2 attack precisely including key dependency by introducing a method "Transition Matrix Computing." Previously, no theoretical security evaluation against χ2 attack was known, it has been done by computer experiments. We should note that it is the first result concerning the way of security evaluation against χ2 attack is shown theoretically.

One-dimensional Cellular Automata (CA's) are considered as potential pseudorandom pattern generators to generate highly random parallel patterns with simple hardware configurations. A class of linear, binary, and of nearest neighbor (radius = 1) CA's is referred to here as elementary ones. This paper investigates operations of such CA's with fixed boundary conditions when non-null boundary values are applied to them. By modifying transition matrices of elementary CA's to include the influence of boundary values, structures of state transition diagrams are determined.