具有范式的局部稳定理论的初等推导问题
Elementary Deduction Problem for Locally Stable Theories with Normal Forms
摘要：
给出了一类局部稳定的范式丰富理论的入侵者演绎问题的判定算法。我们的结果依赖于一个新的和有效的算法来解决一个限制的情况下，高阶关联交换匹配，通过结合AC匹配算法的不同出现和标准算法来解决线性丢番图方程组。自然演绎和微积分之间的转换允许我们使用相同的方法来决定局部稳定理论的\emphelementary演绎问题。作为一个应用程序，我们模型的盲签名理论，并推导出一个算法来决定IDP在这种情况下，扩展以前的可判定性的结果。
英文摘要：
We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative-commutative matching, obtained by combining the Distinct Occurrences of AC- matching algorithm and a standard algorithm to solve systems of linear Diophantine equations. A translation between natural deduction and sequent calculus allows us to use the same approach to decide the \emphelementary deduction problem for locally stable theories. As an application, we model the theory of blind signatures and derive an algorithm to decide IDP in this context, extending previous decidability results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
