Verification analysis of self-verifying automata via semi-tensor product of matrices

The semi-tensor product (STP) of matrices was used in the article, as a new matrix analysis tool, to investigate the problem of verification of self-verifying automata (SVA). SVA is a special variant of finite automata which is essential to nondeterministic communication with a limited number of advice bits. The status, input and output symbols are expressed in vector forms, the dynamic behaviour of SVA is modelled as an algebraic equation of the states and inputs, in which the matrix product is STP. By such algebraic formulation, three necessary and sufficient conditions are presented for the verification problem, by which three algorithms are established to find out all the strings which are accepted, rejected, or unrecognized by a SVA. Testing examples show the correctness of the results.