We consider the problem of the unification modulo an equational theory associativity and commutativity (ACh), which consists of a function symbol h that is homomorphic over an associative–commutative operator +. Since the unification modulo ACh theory is undecidable, we define a variant of the problem called bounded ACh unification. In this bounded version of ACh unification, we essentially bound the number of times h can be applied to a term recursively and only allow solutions that satisfy this bound. There is no bound on the number of occurrences of h in a term, and the + symbol can be applied an unlimited number of times. We give inference rules for solving the bounded version of the problem and prove that the rules are sound, complete, and terminating. We have implemented the algorithm in Maude and give experimental results. We argue that this algorithm is useful in cryptographic protocol analysis.

中文翻译：

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有界 ACh 统一

我们考虑统一模的问题是等式理论结合性和交换性（ACh），它由一个函数符号组成H在结合交换算子 + 上是同态的。由于统一模 ACh 理论是不可判定的，我们定义了问题的一个变体，称为有界 ACh 统一. 在这个有界版本的 ACh 统一中，我们基本上限制了次数H可以递归地应用于一个术语，并且只允许满足这个界限的解决方案。出现的次数没有限制H在一个术语中，+ 符号可以无限次应用。我们给出了解决问题的有界版本的推理规则，并证明这些规则是合理的、完整的和终止的。我们在 Maude 中实现了该算法并给出了实验结果。我们认为该算法在密码协议分析中很有用。