Related papers: Verifying Graph Programs with First-Order Logic (E…
We give formulae for the first homology of the $n$-braid group and the pure 2-braid group over a finite graph in terms of graph theoretic invariants. As immediate consequences, a graph is planar if and only if the first homology of the…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…
Protecting sensitive program content is a critical issue in various situations, ranging from legitimate use cases to unethical contexts. Obfuscation is one of the most used techniques to ensure such protection. Consequently, attackers must…
In this article, we give an overview of our project on higher-order program verification based on HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, we explain how it can be applied to program verification,…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
The first-order (FO) model checking problem asks, given an FO sentence $\phi$ and a graph $G$, whether $G$ is a model of $\phi$. This problem is known to be $\mathsf{AW[*]}$-hard when parameterized by the quantifier rank of the formula. A…
Ensuring the correctness of software for communication centric programs is important but challenging. Previous approaches, based on session types, have been intensively investigated over the past decade. They provide a concise way to…
A grammar formalism based upon CHR is proposed analogously to the way Definite Clause Grammars are defined and implemented on top of Prolog. These grammars execute as robust bottom-up parsers with an inherent treatment of ambiguity and a…
Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
We present a Hoare logic that extends program specifications with regular expressions that capture behaviors in terms of sequences of events that arise during the execution. The idea is similar to session types or process-like behavioral…
Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…
Automatic verification of array manipulating programs is a challenging problem because it often amounts to the inference of in ductive quantified loop invariants which, in some cases, may not even be firstorder expressible. In this paper,…