State space

Algorithm

Algebraic number

Pure mathematics

Discrete mathematics

Statistics

Nondeterministic algorithm

Theoretical computer science

Field (mathematics)

Computer science

Finite-state machine

Automaton

Mathematics

Tensor product

Mathematical analysis

Finite field

Algebra over a field

Science China Information Sciences

Algebraic state space theory (ASST) of logical systems, developed based on the semi-tensor product (STP) which is a new matrix analysis tool built in recent ten years, provides an algebraic analysis approach for many fields of science, such as logical dynamical systems, finite-valued systems, discrete event dynamic systems, and networked game systems. This study focuses on comprehensively surveying the applications of the ASST method to the field of finite state machines (FSMs). Some necessary preliminaries on the method are first reviewed. Then the applications of the method in the FSM field are reviewed, including deterministic FSMs, nondeterministic FSMs, probabilistic FSMs, networked FSMs, and controlled and combined FSMs. In addition, other applications related to both STP and FSMs are surveyed, such as the application of FSM to Boolean control networks and the application of graph theory to FSMs. Finally, some potential research directions with respect to the ASST method in the FSM field are predicted.

Survey on applications of algebraic state space theory of logical systems to finite state machines