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A model of an associative processor names HASP is proposed and described. The objective is to represent associative brain functions in terms of neural network structure. HASP is described with emphasis on its associative memory functions. HASP solved two critical problems which resided in earlier associative memory models: crosstalk noise elimination and multiple-match resolution. HASP eliminates crosstalk noise without complicated orthogonalizing methods. Both problems are solved by the same network structure. With the function of crosstalk noise elimination, the storage capacity increases, and an explosion of crosstalk noise, inevitable in a system such as mutually linked associative networks, can be avoided. With the function of multiple-match resolution, various operations of retrieving information from a memory organized in complicated data structures are possible.