Recognition of Patterns in Periodic Binary Sequences

When humans are presented with information, they tend to search for structure in the information-to encode it, to organize it, to look for regularities. The existence of this structure-seeking behavior can be seen in the behavior of subjects predicting a random sequence of binary events and in the behavior of subjects predicting more highly structured sequences. (A random sequence is a colloquialism for a sequence generated by a mechanism which for two events, 1 and 0, has P{1} = 7r and P{0} = 1 7r. A more highly structured sequence contains additional constraints on conditional probabilities. A completely deterministic sequence is generated by rules of the form "Si -O, 1" where the Si form a mutually exclusive and exhaustive set of states for the events in the sequence, that is, each event follows one and only one state.) Although it is quite clear that subjects search for structure, the details of this structure-seeking behavior continue to elude investigators. In pursuit of models of structure-seeking behavior, investigators have studied behavior on completely deterministic sequences as well as on random and more highly structured sequences. The focus of the present paper will be on models of behavior in experiments using completely deterministic sequences. Two models proposed by other investigators will be reviewed and a third model will be proposed.