Abstract In many verification tasks, system models do not correspond to the focused and idealized models that appear in research literature. In practice, models usually contain components and execution paths that are irrelevant to the property being verified or have only a limited effect on it. Compositional verification presents a practical method for coping with the larger and less targeted models found in such settings. In this paper, we present an automated compositional framework for verifying timed safety properties in networks of timed automata. We show as a main result that the weakest environment assumption, commonly used in compositional reasoning, may in general fail to be recognizable within the timed automata formalism. This negative result motivates shifting the focus to the complement language of violation-inducing timed words, for which we establish recognizability using timed automata with silent transitions. We provide an algorithm for its construction and reduce its size by retaining only the parts directly relevant to the property. The synthesized assumption is later applied to verify the original system. This provides a sound and complete basis for compositional verification of timed automata, including the novel ability to handle automata with multiple clocks and non-deterministic behavior. Our results broaden the applicability of assume–guarantee verification techniques in timed automata and show substantial reductions in the size of the state-space, outperforming monolithic methods on a range of case studies.

Assigning shipping orders to the most appropriate driver in the shortest time but with the highest profit is one of the major concerns of transportation companies. Many studies have been conducted on transportation service procurement systems; however, due to the lack of a framework for modeling human interactions, none of them has used the concept of information diffusion for this purpose. In this article, a monoplex weighted drivers’ collaboration network is developed to model drivers’ relationships within the transportation system. Besides, to identify and track communities during a given time interval of the network, a new community detection algorithm, called dynamic overlapping community detection (DOCD) algorithm, is designed, which can identify viable leaders in each community. In addition to detecting community leaders, the algorithm is able to monitor, assess, and detect the durability of these community leaders over time, which other algorithms are not able to. To evaluate the performance of the algorithm, it is compared with five different algorithms in terms of 14 evaluation measures. The results show the proposed DOCD algorithm outperforms the other algorithms with 88% superiority in the evaluation measures. Then, a fuzzy profit maximization model is developed using information diffused by the identified communities’ viable leaders and information diffusion power of each community. Analyzing a real case study obtains two achievements in the form of “high-risk scenario” and “low-risk scenario” for well-known and novice transportation companies, respectively. Therefore, the obtained results show that transportation companies allocate orders to drivers based on their reputation and risk levels.