Observed Data-Based Model Construction of Finite State Machines Using Exponential Representation of LMs
Yongyi Yan, Jumei Yue, Zengqiang Chen · IEEE Transactions on Circuits & Systems II Express Briefs · 2021
The problem of model construction of finite state machines (FSMs) from observed data is addressed by borrowing the methods and ideas of system identification in control theory. The construction contains three steps. Firstly, the dynamic matrix of FSM to be constructed is built from observed input and output data, the result is a logical matrix (LM). In the second stage, the obtained dynamic matrix is first represented as an exponent of an LM; then the LM is used as the structure matrix of the FSM to be built. Finally, an FSM making the observed data verified the known dynamic equation is constructed according to the one-to-one correspondence between structure matrices and FSMs. In addition, some theoretic results are presented: several necessary and sufficient conditions for the exponent representability of LMs; classification of LMs (LMs are classified into two categories, type-1 and type-2 ones, according to their exponent representability); and methods of representing each kind of LM as an exponent form of an LM.