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The $z$-Transform and Automata-Recognizable Systems of Nonhomogeneous Linear Recurrence Equations over Semirings (1011.1578v1)
Published 6 Nov 2010 in cs.SC and cs.FL
Abstract: A nonhomogeneous system of linear recurrence equations can be recognized by an automaton $\mathcal{A}$ over a one-letter alphabet $A = {z}$. Conversely, the automaton $\mathcal{A}$ generates precisely this nonhomogeneous system of linear recurrence equations. We present the solutions of these systems and apply the $z$-transform to these solutions to obtain their series representation. Finally, we show some results that simplify the series representation of the $z$-transform of these solutions. We consider single systems as well as the composition of two systems.