We investigate decidability, complexity and expressive power issues for (first-order) separation logic with one record field (herein called SL) and its fragments. SL can specify properties about the memory heap of programs with singly-linked lists. Separation logic with two record fields is known to be undecidable by reduction of finite satisfiability for classical predicate logic with one binary relation. Surprisingly, we show that second-order logic is as expressive as SL and as a by-product we get undecidability of SL. This is refined by showing that SL without the separating conjunction is as expressive as SL, whence undecidable too. As a consequence of this deep result, in SL the magic wand can simulate the separating conjunction. By contrast, we establish that SL without the magic wand is decidable with non-elementary complexity by reduction from satisfiability for the first-order theory over finite words. Equivalence between second-order logic and separation logic extends to the case with more than one selector.

Abstract. Handling concurrency using a shared memory and locks is tedious and error-prone. One solution is to use message passing instead. We study here a particular, contract-based flavor that makes the ownership transfer of messages explicit. In this case, ownership of the heap region representing the content of a message is lost upon sending, which can lead to efficient implementations. In this paper, we define a proof system for a concurrent imperative programming language implementing this idea and inspired by the Singularity OS. The proof system, for which we prove soundness, is an extension of separation logic, which has already been used successfully to study various ownership-oriented paradigms.

Abstract. 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 propositional 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.