相关论文: A Few Graph-Based Relational Numerical Abstract Do…
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…
The weakly relational domain of Octagons offers a decent compromise between precision and efficiency for numerical properties. Here, we are concerned with the construction of non-numerical relational domains. We provide a general…
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 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…
Algebraic domains are regions in the plane surrounded by mutually disjoint non-singular real algebraic curves. Poincar'e-Reeb Graphs of them are graphs they naturally collapse: such graphs are formally formulated by Sorea, for example,…
Abstract interpretation-based static analyses rely on abstract domains of program properties, such as intervals or congruences for integer variables. Galois connections (GCs) between posets provide the most widespread and useful formal tool…
Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domains, there exist intuitive definitions of signals and…
We establish a computation-substrate-agnostic inference architecture in which domain is an explicit first-class computational parameter. This produces domain-scoped pruning that reduces per-query search space from O(N) to O(N/K),…
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…
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…
We present a parametric abstract domain for array content analysis. The method maintains invariants for contiguous regions of the array, similar to the methods of Gopan, Reps and Sagiv, and of Halbwachs and Peron. However, it introduces a…
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…
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consists of disjoint smooth connected components of real algebraic plane curves. We study the geometric shape of an algebraic domain by collapsing…
The Abstract Meaning Representation (AMR) is a representation for open-domain rich semantics, with potential use in fields like event extraction and machine translation. Node generation, typically done using a simple dictionary lookup, is…
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…
Qualitative causal relationships compactly express the direction, dependency, temporal constraints, and monotonicity constraints of discrete or continuous interactions in the world. In everyday or academic language, we may express…
We observe algebraic derivations on an affine domain B defined over an algebraically closed field of characteristic 0, which are called locally finite derivations in commutative and non-commutative contexts in other references. We observe…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary signed graphs, and therefore to arbitrary symmetric matrices. We…
An abstract $(v_k,b_r)$-configuration is a pair of finite sets of cardinalities $v$ and $b$ with a relation on the product of the sets such that each element of the first set is related to the same number $k$ of elements from the second set…