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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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等式集合の語問題は,2つの項を与えたときに,等式集合のもとで2つの項が等しいかどうかを決定する問題である.本論文では線形,シャロー,変数非消去かつ非崩壊な規則からなる等式集合の語問題が,等式集合と2つの項から定められる基底項を各等式に代入する変換を用いることにより,変数を持たない等式集合の語問題へ帰着可能であることを示す.この結果より,変数を持たない等式集合の語問題判定アルゴリズムを用いて,目的の語問題を解くことが可能となる. 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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