University of Cambridge > Talks.cam > Logic and Semantics Seminar (Computer Laboratory) > Undecidability of propositional separation logic and its neighbours

Undecidability of propositional separation logic and its neighbours

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Separation logic has become well-established in recent years as an effective formalism for reasoning about memory-manipulating programs. In this talk I shall explain how, and why, it happens that even the purely propositional fragment of separation logic is undecidable. In fact, it turns out that all of the following properties of propositional separation logic formulas are undecidable (among others):

(a) provability in Boolean BI (BBI) and its extensions, even when negation and falsum are excluded;

(b) validity in the class of separation models;

(c) validity in the class of separation models with indivisible units;

(d) validity in any concrete choice of heap-like separation model.

We also gain new insights into the nature of existing decidable fragments of separation logic.

Furthermore, we additionally establish the undecidability of the following properties of propositional formulas, which are related to Classical BI and its ’’dualising’’ resource models:

(e) provability in Classical BI (CBI) and its extensions;

(f) validity in the class of CBI -models;

(g) validity in the class of CBI -models with indivisible units.

All of the above results are new but, in particular, decidability of BBI has been an open problem for some years, while decidability of CBI was a recent open problem.

This is joint work with Max Kanovich, Queen Mary University of London. The talk is based on the paper of the same name which can be found at the speaker’s home page:

http://www.doc.ic.ac.uk/~jbrother

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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