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Mathematics
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Formal Methods in Computer Science: Theory and Applications
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Formal Methods in Computer Science: Theory and Applications

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 2145

Special Issue Editor

Dr. Asieh Salehi Fathabadi

E-Mail Website
Guest Editor
Cyber-Physical Systems Group, University of Southampton, Southampton, UK
Interests: application, tools and methodology for formal methods

Special Issue Information

Dear Colleagues,

Formal methods are increasingly recognized as essential in computer science, offering mathematically rigorous frameworks for the specification, development, and verification of both software and hardware systems. These methods provide the foundation for ensuring correctness, reliability, and security in complex computing systems, which are crucial for a wide range of critical applications. The mathematical underpinnings of formal methods are particularly significant in subfields such as algorithm design, system verification, automated reasoning, and model checking, where they enable precise and robust analysis.

This special issue focuses on the latest mathematical and computational advancements in formal methods within computer science. It aims to present a comprehensive collection of innovative research that not only addresses current theoretical challenges but also explores novel computational techniques and applications. We encourage contributions from researchers in both academia and industry that demonstrate new mathematical models, algorithms, or tools, and their application to real-world problems in areas such as cybersecurity, software engineering, artificial intelligence, and distributed systems.

By highlighting cutting-edge mathematical and computational research, this special issue seeks to foster collaboration and knowledge exchange, paving the way for future breakthroughs in formal methods. We anticipate that this issue will become a valuable resource for researchers and practitioners alike, driving further innovation and deepening the integration of formal methods into the broader landscape of computer science.

Dr. Asieh Salehi Fathabadi
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • formal software engineering
  • theorem proving
  • application of formal methods
  • formal verification
  • model checking
  • mathematical logic
  • formal specification/semantics
  • modeling languages
  • safety-critical systems

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

25 pages, 3597 KiB  
Article
Research on Abstraction-Based Search Space Partitioning and Solving Satisfiability Problems
by Yuexin Huang, Qinzhou Niu and Yanfang Song
Mathematics 2025, 13(5), 868; https://doi.org/10.3390/math13050868 - 5 Mar 2025
Viewed by 391
Abstract
Solving satisfiability problems is central to many areas of computer science, including artificial intelligence and optimization. Efficiently solving satisfiability problems requires exploring vast search spaces, where search space partitioning plays a key role in improving solving efficiency. This paper defines search spaces and [...] Read more.
Solving satisfiability problems is central to many areas of computer science, including artificial intelligence and optimization. Efficiently solving satisfiability problems requires exploring vast search spaces, where search space partitioning plays a key role in improving solving efficiency. This paper defines search spaces and their partitioning, focusing on the relationship between partitioning strategies and satisfiability problem solving. By introducing an abstraction method for partitioning the search space—distinct from traditional assignment-based approaches—the paper proposes sequential, parallel, and hybrid solving algorithms. Experimental results show that the hybrid approach, combining abstraction and assignment, significantly accelerates solving in most cases. Furthermore, a unified method for search space partitioning is presented, defining independent and complete partitions. This method offers a new direction for enhancing the efficiency of SAT problem solving and provides a foundation for future research in the field. Full article
(This article belongs to the Special Issue Formal Methods in Computer Science: Theory and Applications)
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14 pages, 1089 KiB  
Article
On Concatenations of Regular Circular Word Languages
by Bilal Abdallah and Benedek Nagy
Mathematics 2025, 13(5), 763; https://doi.org/10.3390/math13050763 - 26 Feb 2025
Viewed by 223
Abstract
In this paper, one-wheel and two-wheel concatenations of circular words and their languages are investigated. One-wheel concatenation is an operation that is commutative but not associative, while two-wheel concatenation is associative but not commutative. Moreover, two-wheel concatenation may produce languages that are not [...] Read more.
In this paper, one-wheel and two-wheel concatenations of circular words and their languages are investigated. One-wheel concatenation is an operation that is commutative but not associative, while two-wheel concatenation is associative but not commutative. Moreover, two-wheel concatenation may produce languages that are not languages of circular words. We define two classes of regular languages of circular words based on finite automata: in a weakly accepted circular word language, at least one conjugate of each word is accepted by the automaton; in contrast, a strongly accepted language consists of words for which all conjugates are accepted. Weakly accepted circular word languages REGw, in fact, are regular languages that are the same as their cyclic permutations. Strongly accepted circular word languages, REGs, having words with the property that all their conjugates are also in the language, are also regular. We prove that REGw and REGs coincide. We also provide regular-like expressions for these languages. Closure properties of this class are also investigated. Full article
(This article belongs to the Special Issue Formal Methods in Computer Science: Theory and Applications)
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31 pages, 1630 KiB  
Article
A Model Transformation Method Based on Simulink/Stateflow for Validation of UML Statechart Diagrams
by Runfang Wu, Ye Du and Meihong Li
Mathematics 2025, 13(5), 724; https://doi.org/10.3390/math13050724 - 24 Feb 2025
Viewed by 388
Abstract
A model transformation method based on state refinement and semantic mapping is proposed to address the challenges of high modeling complexity and resource consumption in symbolic validation of industrial software requirements. First, a rule-based semantic mapping system is constructed through the explicit definition [...] Read more.
A model transformation method based on state refinement and semantic mapping is proposed to address the challenges of high modeling complexity and resource consumption in symbolic validation of industrial software requirements. First, a rule-based semantic mapping system is constructed through the explicit definition of element correspondence between statechart components and verification models, coupled with a composite state-level refinement strategy to structurally optimize model hierarchy. Second, an automated transformation algorithm is developed to bridge graphical modeling tools with formal verification environments, supported by quantitative evaluation metrics for mapping validity. To demonstrate its practical applicability, the methodology is systematically applied to railway infrastructure safety—specifically the railroad turnout control system—as a critical case study. The experimental implementation converts operational statecharts of turnout control logic into optimized NuSMV models. Not only did the models remain intact, but the state space was also effectively reduced through the optimization of the hierarchical structure. In the validation phase, the converted model is tested for robustness using the fault injection method, and boundary condition anomalies that are not explicitly stated in the requirement specification are successfully detected. The experimental results show that the validation model generated by this method has improved validation efficiency in the NuSMV tool, which is significantly better than the traditional conversion method. Full article
(This article belongs to the Special Issue Formal Methods in Computer Science: Theory and Applications)
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20 pages, 4564 KiB  
Article
A Finite Representation of Durational Action Timed Automata Semantics
by Ahmed Bouzenada, Djamel Eddine Saidouni and Gregorio Díaz
Mathematics 2024, 12(24), 4008; https://doi.org/10.3390/math12244008 - 20 Dec 2024
Viewed by 603
Abstract
Durational action timed automata (daTAs) are state transition systems like timed automata (TAs) that capture information regarding the concurrent execution of actions and their durations using maximality-based semantics. As the underlying semantics of daTAs are infinite due to the modeling of time progress, [...] Read more.
Durational action timed automata (daTAs) are state transition systems like timed automata (TAs) that capture information regarding the concurrent execution of actions and their durations using maximality-based semantics. As the underlying semantics of daTAs are infinite due to the modeling of time progress, conventional model checking techniques become impractical for systems specified using daTAs. Therefore, a finite abstract representation of daTA behavior is required to enable model checking for such system specifications. For that, we propose a finite abstraction of the underlying semantics of a daTA-like region abstraction of timed automata. In addition, we highlight the unique benefits of daTAs by illustrating that they enable the verification of properties concerning concurrency and action duration that cannot be verified using the traditional TA model. We demonstrate mathematically that the number of states in durational action timed automata becomes significantly smaller than the number of states in timed automata as the number of actions increases, confirming the efficiency of daTAs in modeling behavior with action durations. Full article
(This article belongs to the Special Issue Formal Methods in Computer Science: Theory and Applications)
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