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Value-based static analysis techniques express computed program invariants as logical formula over program variables. Researchers and practitioners use these invariants to aid in software engineering and verification tasks. When selecting…
This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…
This article presents a new numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form…
Commutativity of program code (i.e. the equivalence of two code fragments composed in alternate orders) is of ongoing interest in many settings such as program verification, scalable concurrency, and security analysis. While some have…
This article presents the systematic design of a class of relational numerical abstract domains from non-relational ones. Constructed domains represent sets of invariants of the form (vj - vi in C), where vj and vi are two variables, and C…
Recent work by Hermanns et al. and Kattenbelt et al. has extended counterexample-guided abstraction refinement (CEGAR) to probabilistic programs. These approaches are limited to predicate abstraction. We present a novel technique, based on…
The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In…
Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
Relational object invariants (or representation invariants) are relational properties held by the fields of a (memory) object throughout its lifetime. For example, the length of a buffer never exceeds its capacity. Automatic inference of…
Abstract Meaning Representation (AMR) parsing aims to predict an AMR graph from textual input. Recently, there has been notable growth in AMR parsing performance. However, most existing work focuses on improving the performance in the…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…
A parametric analysis is an analysis whose input and output are parametrized with a number of parameters which can be instantiated to abstract properties after analysis is completed. This paper proposes to use Cousot and Cousot's Cardinal…
This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…
The octagon abstract domain is a widely used numeric abstract domain expressing relational information between variables whilst being both computationally efficient and simple to implement. Each element of the domain is a system of…
We present a novel abstractive summarization framework that draws on the recent development of a treebank for the Abstract Meaning Representation (AMR). In this framework, the source text is parsed to a set of AMR graphs, the graphs are…
Variable sharing is a fundamental property in the static analysis of logic programs, since it is instrumental for ensuring correctness and increasing precision while inferring many useful program properties. Such properties include modes,…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…