Edoardo Carta
Edoardo CartaGerardino

Ph.D. (2008) Cornell University

First Position
Dissertation
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Abstract: It is known that a system of linear difference equations with coefficients in a finite ring can be recognized by finite automata. Conversely, the states of a finite automaton over a finite ring can be associated with a system of linear difference equations. We generalize this connection in the natural way: rings are generalized by semirings, difference equations by recurrence equations, and automata by transducers. In order to establish the connection between automata and nonhomogeneous systems of linear recurrence equations with variable coefficients over a semiring, we introduce the concepts of update automaton and update transducer. The linear transformation induced by a nonhomogeneous system is also studied, and solutions for nonhomogeneous systems and the composition of two nonhomogeneous systems are presented. We also explore the Ztransform and power series representation of these solutions.