語問題を基底等式集合の語問題に帰着可能な等式集合のクラスについて

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  • ゴ モンダイ オ キテイ トウシキ シュウゴウ ノ ゴ モンダイ ニ キチャク カノウ ナ トウシキ シュウゴウ ノ クラス ニ ツイテ
  • On class of equation sets whose word problems are reducible to those of ground equation sets

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The word problem of an equation set is to decide, given two terms, whether the two terms are equivalent under the equations. In this paper, we show that word problems of linear, shallow, non-erasing and non-collapsing equation sets are reducible to those of equation sets having no variables, where we use a transformation that substitutes ground terms determined from the equation set and the given two terms into each equation. This result allows us to use decision algorithms for the word problem of an equation set without variables to solve the target problem.

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