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In this paper, we address the problem of safety verification of interval hybrid systems in which the coefficients are intervals instead of explicit numbers. A hybrid symbolic-numeric method, based on SOS relaxation and interval arithmetic…

Symbolic Computation · Computer Science 2013-02-26 Zhengfeng Yang , Min Wu , Wang Lin

Proof by induction plays a critical role in formal verification and mathematics at large. However, its automation remains as one of the long-standing challenges in Computer Science. To address this problem, we developed sem_ind. Given…

Programming Languages · Computer Science 2021-05-11 Yutaka Nagashima

Since the first termination competition in 2004 it is of great interest, whether a proof that has been automatically generated by a termination tool, is indeed correct. The increasing number of termination proving techniques as well as the…

Logic in Computer Science · Computer Science 2012-08-09 Christian Sternagel , René Thiemann , Sarah Winkler , Harald Zankl

Interactive theorem provers are complex systems that require sophisticated platform efforts - and hence systems programming environments - to manage effectively. The Isabelle platform exemplifies this with its Isabelle/Scala systems…

Logic in Computer Science · Computer Science 2024-12-18 Fabian Huch

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…

Numerical Analysis · Mathematics 2017-03-28 John D. Pryce , Nedialko S. Nedialkov , Guangning Tan , Xiao Li

The Isabelle proof assistant includes a small functional language, which allows users to write and reason about programs. So far, these programs could be extracted into a number of functional languages: Standard ML, OCaml, Scala, and…

Programming Languages · Computer Science 2024-09-20 Terru Stübinger , Lars Hupel

Probabilistic model checkers like PRISM only check probabilistic systems of a fixed size. To guarantee the desired properties for an arbitrary size, mathematical analysis is necessary. We show for two case studies how this can be done in…

Logic in Computer Science · Computer Science 2012-12-18 Johannes Hölzl , Tobias Nipkow

Incorrectness Separation Logic (ISL) is a proof system designed to automate verification and detect bugs in programs manipulating heap memories. In this study, we extend ISL to support variable-length array predicates and pointer…

Logic in Computer Science · Computer Science 2025-03-04 Yeonseok Lee , Koji Nakazawa

Creating safe concurrent algorithms is challenging and error-prone. For this reason, a formal verification framework is necessary especially when those concurrent algorithms are used in safety-critical systems. The goal of this guide is to…

Logic in Computer Science · Computer Science 2025-01-24 Elizabeth Dietrich

Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…

Artificial Intelligence · Computer Science 2026-05-08 Baoding He , Zenan Li , Wei Sun , Yuan Yao , Taolue Chen , Xiaoxing Ma , Zhendong Su

For the design and implementation of engineering systems, performing model-based analysis can disclose potential safety issues at an early stage. The analysis of hybrid system models is in general difficult due to the intrinsic complexity…

Systems and Control · Computer Science 2015-01-26 Yi Deng , Agung Julius

A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of…

Mathematical Physics · Physics 2009-10-31 E. S. Cheb-Terrab , A. D. Roche

The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…

Symbolic Computation · Computer Science 2021-06-17 Erika {Á}brahám , James Davenport , Matthew England , Gereon Kremer , Zak Tonks

We present a framework in Isabelle for verifying asymptotic time complexity of imperative programs. We build upon an extension of Imperative HOL and its separation logic to include running time. In addition to the basic arguments, our…

Logic in Computer Science · Computer Science 2018-02-06 Bohua Zhan , Maximilian P. L. Haslbeck

Exception handling is provided by most modern programming languages. It allows to deal with anomalous or exceptional events which require special processing. In computer algebra, exception handling is an efficient way to implement the…

Logic in Computer Science · Computer Science 2014-03-14 Jean-Guillaume Dumas , Dominique Duval , Burak Ekici , Jean-Claude Reynaud

Recently, researchers in answer set programming and constraint programming spent significant efforts in the development of hybrid languages and solving algorithms combining the strengths of these traditionally separate fields. These efforts…

Artificial Intelligence · Computer Science 2013-12-23 Marcello Balduccini , Yulia Lierler

We introduce Mars 2.0 for modeling, analysis, verification and code generation of Cyber-Physical Systems. Mars 2.0 integrates Mars 1.0 with several important extensions and improvements, allowing the design of cyber-physical systems using…

Programming Languages · Computer Science 2024-03-06 Bohua Zhan , Xiong Xu , Qiang Gao , Zekun Ji , Xiangyu Jin , Shuling Wang , Naijun Zhan

In this extended abstract, we discuss the opportunity to formally verify that inference systems for probabilistic programming guarantee good performance. In particular, we focus on hybrid inference systems that combine exact and approximate…

Programming Languages · Computer Science 2023-07-17 Eric Atkinson , Ellie Y. Cheng , Guillaume Baudart , Louis Mandel , Michael Carbin

We present a framework for C code in C11 syntax deeply integrated into the Isabelle/PIDE development environment. Our framework provides an abstract interface for verification back-ends to be plugged-in independently. Thus, various…

Programming Languages · Computer Science 2019-12-24 Frédéric Tuong , Burkhart Wolff

Side-channel attacks, which are capable of breaking secrecy via side-channel information, pose a growing threat to the implementation of cryptographic algorithms. Masking is an effective countermeasure against side-channel attacks by…

Cryptography and Security · Computer Science 2020-06-17 Pengfei Gao , Hongyi Xie , Fu Song , Taolue Chen