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Toward a Theory of problem solving
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algorithm Artificial Intelligence automatic problem solver auxiliary AV goal belonging binary relation cadre called Chapter Chomsky class of equivalence computable function consider construction context-free grammar corresponding Definition described discrete distinctive relation domain Eight-Puzzle elements empiristic evaluation function everywhere defined function example exists fact finite formal grammar function h geometrical object given goal problem Goedel numbering graph heuristic illustrated indexing initial input introduced intuitive language acquisition lattice legal condition linguistic mathematical matrix means method Moreover n-step solution sequence natural language nodes notion obtained operators optimal optimum solution output pair particular patterns phrase marker Politecnico di Milano possible Post's problem present problem F problem schema procedure proof properties prove regular language representation represented problem rhombus Rice's theorem s-m-n theorem satisfies semi-ordering sentence sigma-algebra solving SSPS semantic description SSPS syntactic description standard numbering string structure sub-areas Subchapter subsets successors symbols transformational grammar transformations