Elementary Commonality

Where elementary compositions operate on initial states and acceptance states of DFAs, interference considers their structure. In a DFA, only those paths are relevant which end in an acceptance state. The elementary commonality can, therefore, be understood as the set of paths from initial state to acceptance states which are shared between two DFAs. The result is the intersection operation with the following syntax.

\\Intersection{X0 X1 ... Xn}

matches the intersection of lexemes matched by X0, X1, … Xn.

Together with \Union, \Universe, and \Empty this constitutes the foundation of an algebraic structure as discussed in sec:math-agebra.