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This paper suggests a bidirectional relationship between state-space and problem- reduction representations. It resents a formalism based on multiple-input and multiple-output operators which provides a basis for viewing the two types of representations in this manner. A representation of the language recognition problem which is based on the Cocke parsing algorithm Is used as an illustration. A method for representing problems in first-order logic in such a way that the inference system employed by a resolution-based theorem prover determines whether the set of clauses is interpreted in the state-space mode or in the problem-reduction mode is presented. The analogous concepts in problem-reduction and theorem proving, and the terminology used to refer to them, are noted. The relationship between problem-reduction, input resolution, and linear resolution is is discussed. [ABSTRACT FROM AUTHOR]