Related papers: Global Guidance for Local Generalization in Model …

Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end,…

We consider the problem of checking whether a proposed invariant $\varphi$ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can…

In computational homogenization, a fast solution of the microscopic problem can be achieved by model order reduction in combination with hyper-reduction. Such a technique, which has recently been proposed in the context of magnetostatics,…

Two classical sources of imprecision in static analysis by abstract interpretation are widening and merge operations. Merge operations can be done away by distinguishing paths, as in trace partitioning, at the expense of enumerating an…

Large language models (LLMs) have demonstrated strong reasoning capabilities on math and coding, but frequently fail on symbolic classical planning tasks. Our studies, as well as prior work, show that LLM-generated plans routinely violate…

Local analysis has long been recognised as an effective tool to combat the state-space explosion problem. In this work, we propose a method that systematises the use of local analysis in the verification of deadlock freedom for concurrent…

Owing to the capability of in-context learning, large language models (LLMs) have shown impressive performance across diverse mathematical reasoning benchmarks. However, we find that few-shot demonstrations can sometimes bring negative…

The Model Constructing Satisfiability (MCSat) approach to the SMT problem extends the ideas of CDCL from the SAT level to the theory level. Like SAT, its search is driven by incrementally constructing a model by assigning concrete values to…

This paper presents a sound and complete fault detection approach for cyber-physical systems represented by hidden-mode switched affine models with time varying parametric uncertainty. The fault detection approach builds upon techniques…

Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…

This paper describes a novel unbounded software model checking approach to find errors in programs written in the C language based on incremental SAT-solving. Instead of using the traditional assumption based API to incremental SAT solvers…

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…

In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…

Hyperproperties have shown to be a powerful tool for expressing and reasoning about information-flow security policies. In this paper, we investigate the problem of statistical model checking (SMC) for hyperproperties. Unlike exhaustive…

We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…

This paper studies a fundamental relation that exists between stabilizability assumptions usually employed in distributed model predictive control implementations, and the corresponding notions of invariance implicit in such controllers.…

Model checking is a powerful technique for software verification. However, the approach notably suffers from the infamous state space explosion problem. To tackle this, in this paper, we introduce a novel symbolic method for encoding Petri…

A State Space Model (SSM) is a foundation model in time series analysis, which has recently been shown as an alternative to transformers in sequence modeling. In this paper, we theoretically study the generalization of SSMs and propose…

Inductive invariants are crucial in model checking, yet generating effective inductive invariants automatically and efficiently remains challenging. A common approach is to iteratively analyze counterexamples to induction (CTIs) and derive…