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Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…

Logic in Computer Science · Computer Science 2017-10-03 Ying Jiang , Jian Liu , Gilles Dowek , Kailiang Ji

Many important cryptographic primitives offer probabilistic guarantees of security that can be specified as quantitative hyperproperties; these are specifications that stipulate the existence of a certain number of traces in the system…

Cryptography and Security · Computer Science 2020-05-18 Shubham Sahai , Rohit Sinha , Pramod Subramanyan

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…

Artificial Intelligence · Computer Science 2018-05-23 Rudy Bunel , Ilker Turkaslan , Philip H. S. Torr , Pushmeet Kohli , M. Pawan Kumar

Probabilistic models are a critical part of the modern deep learning toolbox - ranging from generative models (VAEs, GANs), sequence to sequence models used in machine translation and speech processing to models over functional spaces…

Machine Learning · Computer Science 2018-12-10 Krishnamurthy Dvijotham , Marta Garnelo , Alhussein Fawzi , Pushmeet Kohli

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are…

Logic in Computer Science · Computer Science 2017-06-02 Anicet Bart , Benoit Delahaye , Didier Lime , Eric Monfroy , Charlotte Truchet

A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…

Systems and Control · Electrical Eng. & Systems 2024-03-11 Zhi Zhang , Chenyu Ma , Saleh Soudijani , Sadegh Soudjani

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…

Statistics Theory · Mathematics 2011-02-17 Hugo Harari-Kermadec

In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The…

Statistical Finance · Quantitative Finance 2011-11-23 Vladimir Soloviev , Vladimir Saptsin , Dmitry Chabanenko

The formal verification of properties of Hidden Markov Models (HMMs) is highly desirable for gaining confidence in the correctness of the model and the corresponding system. A significant step towards HMM verification was the development by…

Logic in Computer Science · Computer Science 2015-10-29 Noe Hernandez , Kerstin Eder , Evgeni Magid , Jesus Savage , David A. Rosenblueth

Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…

Software Engineering · Computer Science 2025-05-16 Chih-Duo Hong , Anthony W. Lin , Philipp Rümmer , Rupak Majumdar

We give qualitative and quantitative improvements to theorems which enable significance testing in Markov Chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political…

Probability · Mathematics 2019-10-24 Maria Chikina , Alan Frieze , Jonathan Mattingly , Wesley Pegden

This paper presents a comprehensive overview of model validation practices and advancement in the banking industry based on the experience of managing Model Risk Management (MRM) since the inception of regulatory guidance SR11-7/OCC11-12…

Computers and Society · Computer Science 2024-11-12 Agus Sudjianto , Aijun Zhang

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…

Machine Learning · Computer Science 2020-07-15 Jean-Baptiste Tristan , Joseph Tassarotti , Koundinya Vajjha , Michael L. Wick , Anindya Banerjee

As engineered systems expand, become more interdependent, and operate in real-time, reliability assessment is indispensable to support investment and decision making. However, network reliability problems are known to be #P-complete, a…

Data Structures and Algorithms · Computer Science 2019-05-03 R. Paredes , L. Duenas-Osorio , K. S. Meel , M. Y. Vardi

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

Machine Learning · Computer Science 2019-12-20 Aleksandar Bojchevski , Stephan Günnemann

State-of-the-art probabilistic model checkers perform verification on explicit-state Markov models defined in a high-level programming formalism like the PRISM modeling language. Typically, the low-level models resulting from such…

Logic in Computer Science · Computer Science 2021-11-15 Tobias Winkler , Johannes Lehmann , Joost-Pieter Katoen

We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating…

Logic in Computer Science · Computer Science 2023-10-30 Dennis Peuter , Philipp Marohn , Viorica Sofronie-Stokkermans

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before…

Machine Learning · Computer Science 2026-03-25 Rodrigo F. L. Lassance , Jasper De Bock

Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…

Methodology · Statistics 2025-03-14 Matteo D'Alessandro , Magne Thoresen

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…

Programming Languages · Computer Science 2017-04-04 Gilles Barthe , Thomas Espitau , Benjamin Grégoire , Justin Hsu , Pierre-Yves Strub
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