Counting and automata

Counting is widely acknowledged to be one of the most difficult areas of Mathematics. As a result, many programming solutions to counting problems tend to revolve around the brute-force technique of generating all possibilities and testing each for the desired property. Techniques for finding more elegant solutions are presented in Discrete Mathematics courses, but often the mathematical solution can be difficult to find. This paper describes a technique based on Finite State Automata that can be used to create a model for solving counting problems that also produces efficient computing solutions.