Related papers: Invariant Generation through Strategy Iteration in…
While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. 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 dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is…
In this paper we propose a novel methodology for static analysis of binary code using abstract interpretation. We use an abstract domain based on polyhedra and two mapping functions that associate polyhedra variables with registers and…
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…
We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and…
Regular transition systems (RTS) are a popular formalism for modeling infinite-state systems in general, and parameterised systems in particular. In a CONCUR 22 paper, Esparza et al. introduce a novel approach to the verification of RTS,…
We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
To put static program analysis at the fingertips of the software developer, we propose a framework for interactive abstract interpretation. While providing sound analysis results, abstract interpretation in general can be quite costly. To…
This paper is the confluence of two streams of ideas in the literature on generating numerical invariants, namely: (1) template-based methods, and (2) recurrence-based methods. A template-based method begins with a template that contains…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
The discovery of inductive invariants lies at the heart of static program verification. Presently, many automatic solutions to inductive invariant generation are inflexible, only applicable to certain classes of programs, or unpredictable.…
In this paper, a mixed-integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, graph abstractions for resource-constrained agents is presented. The formulation leverages concepts from…
Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is…
We propose a constraint-based flow-sensitive static analysis for concurrent programs by iteratively composing thread-modular abstract interpreters via the use of a system of lightweight constraints. Our method is compositional in that it…
We present in this paper a generic framework for the analysis of multi-threaded programs with recursive procedure calls, synchronisation by rendez-vous between parallel threads, and dynamic creation of new threads. To this end, we consider…
Given a hypergraph $H$, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as $H$ with the minimum number of edges such that the subgraph induced by every hyperedge of $H$ is connected. This problem has…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…