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This paper presents an automatic approach to a non-cryptographic hash function design based on grammar guided genetic programming. The paper describes how it is possible to design a non-cryptographic hash function, implementation issues such as terminal and nonterminal symbols, fitness measure, and used context-free grammar. The main aim of this paper is to link the expert knowledge in the design of non-cryptographic hash function and the process of automatic design which can try many more combinations then an expert can. The hash function automatically designed in the paper is competitive with human design and it is compared with the most used non-cryptographic hashes in the field of speed of processing and in the field of collision resistance. The results are discussed in the last section and further improvement is mentioned.