Mathematical analysis of dialogue control strategies

In this paper we describe a quantitative relation between the e ciency of dialogue control strategies, we measure by the average number of exchanges taken during a dialogue, and the performance of a speech recognition system used in a spoken dialogue system. We consider four dialogue control strategies: (1) direct con rmation, (2) indirect con rmation, (3) multiple item answer followed by direct con rmations, and (4) multiple item answer followed by multiple item con rmations. If n information items are necessary to execute a task, a status of a dialogue is represented by a triplet (u; k; c) (u + k + c = n), where u, k and c are the numbers of unknown, known not yet con rmed, and con rmed items respectively. The mathematical analyses of the strategies are based on the fact that the state transition of a dialogue can be represented by a Markov process in which a space of states are a set of triplets (u; k; c), and state transition probabilities are decided by a speech recognition rate and user's behaviors.