Analysis of software specifications based on statistics of Markov chain

In this paper, an innovative method to analyze the software specifications by using a model based on the Markov Chain is proposed. It is well known that all kinds of software are executed via the instruction set of the processor. Since the instruction set can be classified and divided into a series of finite state (i.e. the finite-state machine), it is natural that the software programs based on it has different corresponding characteristics of the Markov process in each state. More importantly, the transition probability can be calculated through the Markov chain in the form of different sparse matrix and with the help of the Discrete Fourier Transform (DFT), the model of the software can be acquired. Once the modeling is done, it will be possible to optimize the software both in the hardware design and the compiling process, which differs from the usual optimization applied only during the hardware designing process. Experimental results have shown that the model is able to greatly reduce the difficulty in solving the problems of the hit rate, cache consistency, etc.