مطالب

The verification of complex systems has traditionally relied on semi-automatic theorem-proving methods. However, model checking represents a paradigm shift by enabling automated, exhaustive verification of behavioral properties through systematic state exploration. Among advanced formal verification tools, Colored Petri Net (CPN) stands out for its integration of the ML programming language, facilitating robust model checking and system validation. Nevertheless, the application of CPN to complex systems is often constrained by the state-space explosion problem, which presents a significant challenge in contemporary research. While state-space analysis offers powerful capabilities for validation and scenario extraction, its potential remains largely untapped due to computational complexity constraints. This limitation is particularly pronounced in concurrent systems with multiple interacting variables, exemplified by game systems where intricate rule sets, deadlock conditions, and termination scenarios demand sophisticated modeling approaches. This paper presents a novel methodological framework for modeling and analyzing such game riddles, introducing methods to mitigate the state-space explosion problem. We demonstrate the efficacy of our approach through a comprehensive case study of the Merchant Ship puzzle game, though the methodology generalizes across various game typologies. By synthesizing model-checking techniques with ML-based algorithmic implementations, we develop an optimized search strategy for traversing the state space graph, enabling the derivation of quantitative complexity metrics. These metrics encompass critical indicators such as the success-to-total scenario ratio and the minimal trajectory length for both successful and unsuccessful game completions. Our research contributes to both the theoretical understanding of game complexity analysis and practical applications in game design through formal methods.

This paper addresses the contemporary crisis of Islam in relation to the use of social media, aiming to study the religious and doctrinal concepts disseminated across several Islamic websites. The objective is to identify the most prominent electronic networks contributing to the process of Islamic preaching and guidance, and to highlight the concepts, beliefs, and jurisprudential rulings they offer. Furthermore, the paper examines the extent to which these contents align with the core values of Islam, as well as their impact on audiences and followers. It also explores the challenges associated with utilizing these platforms to spread the Islamic message. The research on this topic required the use of various methodologies, such as the historical and descriptive approaches. Additionally, the comparative method was employed to present examples of moderate Islamic websites and to compare jurisprudential rulings with other Islamic sources in the case study. This study revealed numerous controversial issues presented by Islamic websites, based on various sources related to the Prophet’s traditions and the accounts of the Companions. These issues represent one of the main causes of the contemporary crisis in Islam, which is the focus of this study. the adoption of extreme religious discourse promoted by these websites, along with the vilification of Islamic websites that may differ in some rulings, perspectives, and religious jurisprudence, leads to a deviation from the goal toward which humanity should be heading—establishing a tolerant divine message.