We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists.

中文翻译：

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分离逻辑片段的组合蕴涵检查

我们提出了一种用于检查分离逻辑公式之间的蕴涵的决策过程，其中归纳谓词指定了对应于各种单链表的有限嵌套的复杂数据结构：非循环或循环、嵌套列表、跳过列表等。决策过程在从某种意义上说，它将检查两个任意公式之间的蕴涵问题简化为检查公式和原子之间的蕴涵问题。随后，如果原子是谓词，我们将蕴涵减少到测试从谓词派生的树自动机语言中的公式派生的树的成员资格。该过程后来也扩展到双向链表。