The list segment predicate ls used in separation logic for verifying programs with pointers is well suited to express properties on singly-linked lists. We study the effects of adding ls to the full quantifier-free separation logic with the separating conjunction and implication, which is motivated by the recent design of new fragments in which all these ingredients are used indifferently and verification tools start to handle the magic wand connective. This is a very natural extension that has not been studied so far. We show that the restriction without the separating implication can be solved in polynomial space by using an appropriate abstraction for memory states, whereas the full extension is shown undecidable by reduction from first-order separation logic. Many variants of the logic and fragments are also investigated from the computational point of view when ls is added, providing numerous results about adding reachability predicates to quantifier-free separation logic.

中文翻译：

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在无量词分离逻辑中添加可达性谓词的效果

列表段谓词 ls 在分离逻辑中用于验证带有指针的程序，非常适合表示单链表上的属性。我们研究了将 ls 添加到带有分离连词和蕴涵的完整无量词分离逻辑中的效果，这是由最近设计的新片段所推动的，其中所有这些成分都被冷漠地使用，并且验证工具开始处理魔术棒连接词. 这是一个非常自然的扩展，到目前为止还没有研究过。我们表明，可以通过对记忆状态使用适当的抽象在多项式空间中解决没有分离含义的限制，而通过从一阶分离逻辑的简化显示完整扩展是不可判定的。