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This paper shows how the nondirectional structural analysis of pattern data can be performed by matching a problem reduction representation (PRR) of pattern structure with sample data, using a best-first state space search algorithm called SSS*. The end result of the matching algorithm is a tree whose nodes represent recognized structures in the data. Tip nodes of the tree structure correspond to primitives which are recognized in the raw data by curve fitting routines. The operators of the algorithm allow the tree to be constructed with a combination of top-down or bottom-up steps. The matching of the structure tree to waveform segments need not be done in a left-right sequence. Moreover ambiguous matches are pursued in a best first order by using state space search with partial parse trees as states. A software system called WAPSYS (for waveform parsing system) is described, which implements this structural analysis paradigm. Experience using WAPSYS to analyze carotid pulse waves is also discussed.