Philipp Rümmer

Chencheng Liang, Philipp Rümmer, Marc Brockschmidt

Learning program semantics from raw source code is challenging due to the complexity of real-world programming language syntax and due to the difficulty of reconstructing long-distance relational information implicitly represented in programs using identifiers. Addressing the first point, we consider Constrained Horn Clauses (CHCs) as a standard representation of program verification problems, providing a simple and programming language-independent syntax. For the second challenge, we explore graph representations of CHCs, and propose a new Relational Hypergraph Neural Network (R-HyGNN) architecture to learn program features. We introduce two different graph representations of CHCs. One is called constraint graph (CG), and emphasizes syntactic information of CHCs by translating the symbols and their relations in CHCs as typed nodes and binary edges, respectively, and constructing the constraints as abstract syntax trees. The second one is called control- and data-flow hypergraph (CDHG), and emphasizes semantic information of CHCs by representing the control and data flow through ternary hyperedges. We then propose a new GNN architecture, R-HyGNN, extending Relational Graph Convolutional Networks, to handle hypergraphs. To evaluate the ability of R-HyGNN to extract semantic information from programs, we use R-HyGNNs to train models on the two graph representations, and on five proxy tasks with increasing difficulty, using benchmarks from CHC-COMP 2021 as training data. The most difficult proxy task requires the model to predict the occurrence of clauses in counter-examples, which subsumes satisfiability of CHCs. CDHG achieves 90.59% accuracy in this task. Furthermore, R-HyGNN has perfect predictions on one of the graphs consisting of more than 290 clauses. Overall, our experiments indicate that R-HyGNN can capture intricate program features for guiding verification problems.

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Julie Cailler et al.

This paper proposes a Graph Neural Network-guided algorithm for solving word equations, based on the well-known Nielsen transformation for splitting equations. The algorithm iteratively rewrites the first terms of each side of an equation, giving rise to a tree-like search space. The choice of path at each split point of the tree significantly impacts solving time, motivating the use of Graph Neural Networks (GNNs) for efficient split decision-making. Split decisions are encoded as multi-classification tasks, and five graph representations of word equations are introduced to encode their structural information for GNNs. The algorithm is implemented as a solver named DragonLi. Experiments are conducted on artificial and real-world benchmarks. The algorithm performs particularly well on satisfiable problems. For single word \mbox{equations}, DragonLi can solve significantly more problems than well-established string solvers. For the conjunction of multiple word equations, DragonLi is competitive with state-of-the-art string solvers.

Zafer Esen, Philipp Rümmer, Tjark Weber

Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel invariant-based heap encoding leveraging uninterpreted predicates and prophecy variables to reduce verification of heap-manipulating programs to verification of programs over integers only. Our encoding of heap is general and agnostic to specific data structures. To the best of our knowledge, our approach is the first heap invariant-based method that achieves both soundness and completeness. We provide formal proofs establishing the correctness of our encodings. Through an experimental evaluation, we demonstrate that time-indexed heap invariants significantly extend the capability of existing verification tools, allowing automatic verification of programs with heap that were previously out of reach for state-of-the-art tools.

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Julie Cailler et al.

Nielsen transformation is a standard approach for solving word equations: by repeatedly splitting equations and applying simplification steps, equations are rewritten until a solution is reached. When solving a conjunction of word equations in this way, the performance of the solver will depend considerably on the order in which equations are processed. In this work, the use of Graph Neural Networks (GNNs) for ranking word equations before and during the solving process is explored. For this, a novel graph-based representation for word equations is presented, preserving global information across conjuncts, enabling the GNN to have a holistic view during ranking. To handle the variable number of conjuncts, three approaches to adapt a multi-classification task to the problem of ranking equations are proposed. The training of the GNN is done with the help of minimum unsatisfiable subsets (MUSes) of word equations. The experimental results show that, compared to state-of-the-art string solvers, the new framework solves more problems in benchmarks where each variable appears at most once in each equation.

Chih-Duo Hong, Anthony W. Lin, Rupak Majumdar et al.

Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot of work on verifying probabilistic bisimulation for finite systems. This is however not the case for parameterized systems, where the problem is in general undecidable. In this paper we provide a generic framework for reasoning about probabilistic bisimulation for parameterized systems. Our approach is in the spirit of software verification, wherein we encode proof rules for probabilistic bisimulation and use a decidable first-order theory to specify systems and candidate bisimulation relations, which can then be checked automatically against the proof rules. As a case study, we show that our framework is sufficiently expressive for proving the anonymity property of the parameterized dining cryptographers protocol and the parameterized grades protocol, when supplied with a candidate regular bisimulation relation. Both of these protocols hitherto could not be verified by existing automatic methods. Moreover, with the help of standard automata learning algorithms, we show that the candidate relations can be synthesized fully automatically, making the verification fully automated.