State enumeration with abstract descriptions of state machines

We propose a theory of abstract descriptions of state machines in a many-sorted rst-order logic with abstract and concrete sorts. State variables containing data values have abstract sorts while control state variables have concrete sorts. Data operations are represented by uninterpreted function symbols. The theory provides a foundation for automated state enumeration methods whose complexity is independent of the width of the data path, and in particular for methods based on Multiway Decision Grahps (MDGs).