A Characterization of Associativity

A necessary and sufficient condition for the associativity of a function is given, in terms of a particular relation being a function. The concept of an associative function is generalized to the concept of a function being associative relative to a sequence and a characterization of such relative associativity is also given. These two characterizations are applied to the problem ofproving the associativity, or relative associativity, of a function.
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Charlesworth, Arthur. "A Characterization of Associativity." University of Virginia Institute for Parallel Computation Tech Report (1990).