Formalization of origami and origami-programming based on algebraic graph rewriting

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Abstraction of paper fold (origami) and establishment of a formal theory of fold are our ultimate goal. Towards that goal, we formalized origami by algebraic graph rewriting theory and verified certain geometrical propertiesof origami. The results we obtained are as follows:(1) We develop a graph rewriting language for origami and its interpreter.(2) In order to concretize the graph rewriting to be used to simulate actual origami and to verify geometrical properties, we developed algorithms for transformingbasic folds to algebraic expressions.(3) In parallel with the above developments we extended and improved e-origami system Eos that we have developed. The extension enables us to automatically verify more geometrical theorems and to speed up the computation of proving.