Concepts of Optimal Utterance in Dialogue: Selection and Complexity

Dialogue protocols have been the subject of considerable attention with respect to their potential applications in multiagent system environments. Formalisations of such protocols define classes of dialogue locutions, concepts of a dialogue state, and rules under which a dialogue proceeds. One important consideration in implementing a protocol concerns the criteria an agent should apply in choosing which utterance will constitute its next contribution: ideally, an agent should select a locution that (by some measure) optimises the outcome. The precise interpretation of optimise may vary greatly depending on the nature and intent of a dialogue area. One option is to choose the locution that results in a minimal length debate. We present a formal setting for considering the problem of deciding if a particular utterance is optimal in this sense and show that this decision problem is both NP–hard and CO-NP–hard.