State-Space, Problem-Reduction, and Theorem Proving-Some Relationships This paper suggests a bidirectional relationship between state-space and problem-reduction representations. It presents 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-spacer 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 discussed. CACM February, 1975 VanderBrug, G. J. Minker, J. artificial intelligence, state-space representation, problem-reduction representation, theorem proving, language recognition 3.64 CA750205 JB January 12, 1978 8:27 AM 2794 5 2794 2794 5 2794 2794 5 2794