5 research outputs found
Graph-Based Shape Analysis Beyond Context-Freeness
We develop a shape analysis for reasoning about relational properties of data
structures. Both the concrete and the abstract domain are represented by
hypergraphs. The analysis is parameterized by user-supplied indexed graph
grammars to guide concretization and abstraction. This novel extension of
context-free graph grammars is powerful enough to model complex data structures
such as balanced binary trees with parent pointers, while preserving most
desirable properties of context-free graph grammars. One strength of our
analysis is that no artifacts apart from grammars are required from the user;
it thus offers a high degree of automation. We implemented our analysis and
successfully applied it to various programs manipulating AVL trees,
(doubly-linked) lists, and combinations of both
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
Unified Reasoning About Robustness Properties of Symbolic-Heap Separation Logic
The final publication is available via https://doi.org/10.1007/978-3-662-54434-1_23.We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability, reachability, and acyclicity, are important for a wide range of reasoning tasks in automated program analysis and verification based on separation logic. Previously, such properties have appeared in many places in the separation logic literature, but have not been studied in a systematic manner. In this paper, we develop an algorithmic framework based on heap automata that allows us to derive asymptotically optimal decision procedures for a wide range of robustness properties in a uniform way.We implemented a prototype of our framework and obtained promising results for all of the aforementioned robustness properties.Further, we demonstrate the applicability of heap automata beyond robustness properties. We apply our algorithmic framework to the model checking and the entailment problem for symbolic-heap separation logic.Austrian Science Funds (FWF)Deutsche Forschungsgemeinschaft (DFG