We extend order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The obtained signature corresponds to a finite bottom-up unranked tree automaton. We prove that regular expression order-sorted (REOS) unification is of type infinitary and decidable. The unification problem presented by us generalizes some known problems, such as, e.g., order-sorted unification for ranked terms, sequence unification, and word unification with regular constraints. Decidability of REOS unification implies that sequence unification with regular hedge language constraints is decidable, generalizing the decidability result of word unification with regular constraints to terms. A sort weakening algorithm helps to construct a minimal complete set of REOS unifiers from the solutions of sequence unification problems. Moreover, we design a complete algorithm for REOS matching, and show that this problem is NP-complete and the corresponding counting problem is #P-complete.

通过允许对变量和函数符号进行正则表达式排序，我们扩展了按顺序排序的统一。获得的签名对应于有限的自底向上的未排序树自动机。我们证明了正则表达式顺序排序（REOS）统一类型是无限的和可判定的。我们提出的统一问题概括了一些已知问题，例如，排序术语的排序排序统一，序列统一和具有常规约束的单词统一。REOS统一的可判定性意味着具有规则对冲语言约束的序列统一是可判定的，从而将具有规则约束的词统一的可判定性结果推广到术语上。排序弱化算法有助于从序列统一问题的解决方案中构造最小的REOS统一体集合。此外，我们设计了一个完整的REOS匹配算法，证明该问题是NP完全的，相应的计数问题是#P完整的。