Related papers: Interpolation Properties and SAT-based Model Check…
In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
This paper discusses how model checking, a technique used for the verification of behavioural requirements of dynamic systems, can be usefully deployed for the verification of contracts. A process view of agreements between parties is…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting…
We formalize a problem we call combinatorial pair testing (CPT), which has applications to the identification of uncooperative or unproductive participants in pair programming, massively distributed computing, and crowdsourcing…
Context: The complexity of modern safety-critical systems in industries keep on increasing due to the rising number of features and functionalities. This calls for formal methods in order to entrust confidence in such systems. Nevertheless,…
Clustering algorithms are an essential part of the unsupervised data science ecosystem, and extrinsic evaluation of clustering algorithms requires a method for comparing the detected clustering to a ground truth clustering. In a general…
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result,…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
In this article, a model-theoretic approach is proposed to prove that the first-order G\"odel logic, $\mathbf{G}$, as well as its extension $\mathbf{G}^\Delta$ associated with first-order relational languages enjoy the Craig interpolation…
Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a…
In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…
Certification helps to increase trust in formal verification of safety-critical systems which require assurance on their correctness. In hardware model checking, a widely used formal verification technique, phase abstraction is considered…
Classical approximation and learning methods are typically optimized for interpolation over a sampled domain {\Omega}, with no guarantees on their behavior in an extrapolation region {\Xi}, where small in-domain errors may amplify. We…
As large language models (LLMs) have gained popularity for a variety of use cases, making them adaptable and controllable has become increasingly important, especially for user-facing applications. While the existing literature on LLM…
We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series…