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In this paper we prove several results concerning this complexity measure. First we establish (in a non-constructive manner) that there exist languages which cannot be recognized with less than n communication (obviously, communication n is always enough for recognizing any language). In fact, we show that for any functionf(n) < n, there are languages recognizable with communicationf(n) but not with communicationf (n)-1. In other words, this complexity measure possesses a very dense hierarchy or complexity classes, as miniscule increments in communication add to the languages that can be recognized.
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Papadimitriou et al. (1982) studied this question.