Infinite linear sequential machines

摘要

Linear sequential machines (LSM's for short) are considered over arbitrary fields. Various finiteness conditions are given for, sequential machines and LSM's with these properties are characterized. It is shown that the set of all input/output pairs characterizes an LSM. The effect on realizations of varying the ground field is studied. A number of algorithms are given, for the solution of specific problems. Decision procedures are given for the equivalence problem for LSM's. The problem of determining if one state is accessible from another is discussed and a number of results are presented.