1,065 research outputs found
Deciding Entailments in Inductive Separation Logic with Tree Automata
Separation Logic (SL) with inductive definitions is a natural formalism for
specifying complex recursive data structures, used in compositional
verification of programs manipulating such structures. The key ingredient of
any automated verification procedure based on SL is the decidability of the
entailment problem. In this work, we reduce the entailment problem for a
non-trivial subset of SL describing trees (and beyond) to the language
inclusion of tree automata (TA). Our reduction provides tight complexity bounds
for the problem and shows that entailment in our fragment is EXPTIME-complete.
For practical purposes, we leverage from recent advances in automata theory,
such as inclusion checking for non-deterministic TA avoiding explicit
determinization. We implemented our method and present promising preliminary
experimental results
On Automated Lemma Generation for Separation Logic with Inductive Definitions
Separation Logic with inductive definitions is a well-known approach for
deductive verification of programs that manipulate dynamic data structures.
Deciding verification conditions in this context is usually based on
user-provided lemmas relating the inductive definitions. We propose a novel
approach for generating these lemmas automatically which is based on simple
syntactic criteria and deterministic strategies for applying them. Our approach
focuses on iterative programs, although it can be applied to recursive programs
as well, and specifications that describe not only the shape of the data
structures, but also their content or their size. Empirically, we find that our
approach is powerful enough to deal with sophisticated benchmarks, e.g.,
iterative procedures for searching, inserting, or deleting elements in sorted
lists, binary search tress, red-black trees, and AVL trees, in a very efficient
way
Spatial Interpolants
We propose Splinter, a new technique for proving properties of
heap-manipulating programs that marries (1) a new separation logic-based
analysis for heap reasoning with (2) an interpolation-based technique for
refining heap-shape invariants with data invariants. Splinter is property
directed, precise, and produces counterexample traces when a property does not
hold. Using the novel notion of spatial interpolants modulo theories, Splinter
can infer complex invariants over general recursive predicates, e.g., of the
form all elements in a linked list are even or a binary tree is sorted.
Furthermore, we treat interpolation as a black box, which gives us the freedom
to encode data manipulation in any suitable theory for a given program (e.g.,
bit vectors, arrays, or linear arithmetic), so that our technique immediately
benefits from any future advances in SMT solving and interpolation.Comment: Short version published in ESOP 201
Tractability of Separation Logic with Inductive Definitions: Beyond Lists
In 2011, Cook et al. showed that the satisfiability and entailment can be checked in polynomial time for a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. In this paper, we investigate whether the tractability results can be extended to more expressive fragments of separation logic that allow defining data structures beyond linked lists. To this end, we introduce separation logic with a simply-nonlinear compositional inductive predicate where source, destination, and static parameters are identified explicitly (SLID[snc]). We show that if the inductive predicate has more than one source (destination) parameter, the satisfiability problem for SLID[snc] becomes intractable in general. This is exemplified by an inductive predicate for doubly linked list segments. By contrast, if the inductive predicate has only one source (destination) parameter, the satisfiability and entailment problems for SLID[snc] are tractable. In particular, the tractability results hold for inductive predicates that define list segments with tail pointers and trees with one hole
Entailment Checking in Separation Logic with Inductive Definitions is 2-EXPTIME hard
The entailment between separation logic formulae with inductive predicates,
also known as symbolic heaps, has been shown to be decidable for a large class
of inductive definitions. Recently, a 2-EXPTIME algorithm was proposed and an
EXPTIME-hard bound was established; however no precise lower bound is known. In
this paper, we show that deciding entailment between predicate atoms is
2-EXPTIME-hard. The proof is based on a reduction from the membership problem
for exponential-space bounded alternating Turing machines
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