Lineare Realisierbarkeit endlicher Automaten über endlichen Körpern

Summary

After having compiled basic concepts (§ 1) we give a necessary and sufficient condition under which a finite sequential machine a is K-linearly realizable where K is a finite field (§ 2, Erster Hauptsatz). This theorem enables us to define a system of linear equations with integer coefficients, the so-called characteristic system of a, which gives the possibility to decide whether or not a is K-linearly realizable (§ 3). Research about divisors of certain determinants constructed with the help of the characteristic system gives us a survey about all finite fields K having the property that a is K-linearly realizable (§§ 4, 5).