You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: We present a (semi-)decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of linked lists: acyclic or cyclic, singly or doubly linked, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using singly and doubly linked nested lists as well as skip lists.

[2]: 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.

[3]:
The tool SLIDE [3] [2] provides decision procedures for fragments of SL based on reductions to the language inclusion problem of tree automata. Their fragments contain no data or size constraints. In addition, the EXPTIME lower bound complexity is an important obstacle for scalability. Our previous work [1] introduces a decision procedure based on reductions to the membership problem of tree automata which however is not capable of dealing with data constraints.