The Structure and Two Complexities of Economic Choice Semiautomata
نویسنده
چکیده
The structure of choice implementing semiautomata is characterized. In contrast to the more commonly used directed graph representation of the semiautomaton, the primary representation here is as a transformation semigroup. For convenience the means for determining the directed graph representation also is presented. Associated with the choice implementing semiautomata are two complexities; algebraic complexity, which is linked to the mathimatical power required to implement choice and computational complexity, which is determined by the difficulty of constructing a particular choice semiautomaton. Each of these complexities is demonstrated to be associated with the type of consistency axiom satisfied by the choice function being imp;emented by the semjiautomaton. Moreover, these two complexities are demonstrated to be dual to each other.
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