Mathematics in Formal Methods and Model Checking

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 14 June 2026 | Viewed by 404

Special Issue Editor


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Guest Editor
Department of Computer Science and Engineering, University of Gothenburg and Chalmers University of Technology, Gothenburg, Sweden
Interests: concurrency and control theory; synthesis and formal verification

Special Issue Information

Dear Colleagues,

This Special Issue collects high-quality original research papers on “Mathematics in Formal Methods and Model Checking”. It aims to bring together researchers and practitioners interested in automated tool-based techniques for the analysis of software as well as models of software for the purpose of verification and validation. The Special Issue specifically focuses on the analysis of both concurrent and sequential software. Submissions are solicited on theoretical results, novel algorithms, tool development, and empirical evaluation.

The Special Issue also welcomes software analysis using any automated techniques, including model checking, automated theorem proving, and symbolic execution.

Topics of interest include, but are not limited to, the following:

Formal verification techniques for the automated analysis of (concurrent) software/hardware, including

  • Model checking;
  • Deductive verification;
  • Automated theorem proving, including SAT and SMT;
  • Abstraction and symbolic execution techniques;
  • Static analysis and abstract interpretation;
  • Modular and compositional verification techniques;
  • Verification of timed and probabilistic systems;
  • Automated testing using advanced analysis techniques;
  • Program synthesis;
  • Derivation of specifications, test cases etc. via formal analysis;
  • Formal specification languages, temporal logic, design-by-contract;
  • Implementation of novel verification tools;
  • Benchmarks and comparative studies for verification tools.

Dr. Yehia Abd Alrahman
Guest Editor

Manuscript Submission Information

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Keywords

  • formal methods
  • model checking
  • automated reasoning

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Published Papers (1 paper)

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Research

20 pages, 536 KB  
Article
The Machine-Checked Complete Formalization of Landau’s Foundations of Analysis in Rocq
by Yue Guan, Yaoshun Fu and Xiangtao Meng
Mathematics 2026, 14(1), 61; https://doi.org/10.3390/math14010061 - 24 Dec 2025
Abstract
Formal verification has achieved remarkable outcomes in both theory advancement and engineering practice, with the formalization of mathematical theories serving as its foundational cornerstone—making this process particularly critical. Axiomatic set theory underpins modern mathematics, providing the rigorous basis for constructing almost all theories. [...] Read more.
Formal verification has achieved remarkable outcomes in both theory advancement and engineering practice, with the formalization of mathematical theories serving as its foundational cornerstone—making this process particularly critical. Axiomatic set theory underpins modern mathematics, providing the rigorous basis for constructing almost all theories. Landau’s Foundations of Analysis starts with pure logical axioms from set theory, does not rely on geometric intuition, strictly constructs number systems, and is a benchmark for axiomatic analysis in modern mathematics. In this paper, we first develop a machine proof system for axiomatic set theory rooted in the Morse–Kelley(MK) system. This system encompasses effective proof automation, scale simplification, and specialized handling of the classification axiom for ordered pairs. We then prove the Transfinite Recursion Theorem, leveraging it to further prove the Recursion Theorem for natural numbers—the key result for defining natural number operations. Finally, we detail the implementation of a machine proof system for analysis, which adopts MK as its description language and adheres to Landau’s Foundations of Analysis. This formalization realized all the contents of the book from natural numbers to complex numbers. All formalization does not need to introduce the standard library and has undergone verification by Rocq(Coq) 8.16 to ensure reliability. Implemented using the Rocq proof assistant, the formalization has undergone verification to ensure reliability. This work holds broader applicability such as the formalization of point-set topology and abstract algebra, while also serving as a valuable resource for teaching axiomatic set theory and mathematical analysis. Full article
(This article belongs to the Special Issue Mathematics in Formal Methods and Model Checking)
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