The Effects of Adding Reachability Predicates in Propositional Separation Logic

International audienceThe 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 proposi-tional 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 propositional separation logic

A Theory of Singly-Linked Lists and its Extensible Decision Procedure

The key to many approaches to reason about pointerbased data structures is the availability of a decision procedure to automatically discharge proof obligations in a theory encompassing data, pointers, and the reachability relation induced by pointers. So far, only approximate solutions have been proposed which abstract either the data or the reachability component. Indeed, such approximations cause a lack of precision in the verification techniques where the decision procedures are exploited. In this paper, we consider the pointer-based data structure of singly-linked lists and define a Theory of Linked Lists (TLL). The theory is expressive since it is capable of precisely expressing both data and reachability constraints, while ensuring decidability. Furthermore, its decidability problem is NP-complete. We also design a practical decision procedure for TLL which can be combined with a wide range of available decision procedures for theories in firstorder logic