Reaction systems (RS) are a model of computation that was inspired by biochemical reactions in living cells. RS are open dynamical systems: while the computation of the next state is deterministic, the conditions triggering the computation depend on the behaviour of an external (uncontrollable) environment. Moreover, although RS have been introduced as a qualitative modelling framework, recent algebraic formalisation have made it possible to extend their expressiveness with quantitative information, like duration of reactions and linear dependencies between the quantities of entities. However, no formal framework for the analysis of such quantitative information is available in the literature. The Stark tool has been introduced to model and analyse the behaviour of dynamical systems interacting with an unpredictable environment. Thanks to its simplicity and versatility, Stark has been successfully applied in a variety of studies, including establishing safety guarantees for autonomous driving systems, ensuring the effectiveness of digital twins, and verifying robustness properties of biochemical systems. In this paper we show how we can implement (quantitative) RS in Stark and exploit the tool to automate their analysis. We apply our approach to three case studies: lac operon expression and synaptic transmission between two and three neurons.
Cooperative path planning for multiple UAVs constitutes a constrained multi-objective optimization problem characterized by intricate physical constraints and conflicting objectives. Existing multi-objective evolutionary algorithms struggle to balance constraint satisfaction and objective optimization simultaneously in cooperative multi-UAV path planning, leading to degraded solution feasibility, convergence, and diversity. To address these limitations, a multitasking three-stage constrained heuristic evolutionary algorithm (MTCHEA) is proposed for cooperative UAV path planning. The algorithm decomposes the constrained multi-objective path planning problem into a main task and an auxiliary task, balancing constraint satisfaction with objective optimization through task collaboration and a three-stage adaptive mechanism. Exploration and exploitation are coordinated using hybrid differential evolution guided by the Maximum Minimum Euclidean Distance (MMED) indicator, and path optimization operators are designed to accommodate UAV physical constraints. The proposed algorithm is evaluated on simulated terrains with different levels of complexity and on a real-world scenario based on DEM data from Zijingguan Town, Yixian County, Hebei Province. Comparative results against MOPSO, NSGA-II, SHMODE, M2M-DW, and TCHM-MOEA demonstrate clear advantages in feasible-solution ratio, hypervolume, diversity, and path length, indicating strong convergence behavior, well-distributed solutions, and robust constraint-handling performance.
This work identifies one-dimensional, d-state, m-neighborhood finite Cellular Automata (CAs) exhibiting fixed-point and multi-length attractors under periodic boundary conditions. We utilize the primary RMT sets to develop some theories that characterize such CAs. By applying these theorems, the presence of fixed-points or multi-length attractors upto length d^m-1 in a CA can be determined in linear time. Then we conduct a case study on the first degree CAs (FDCAs) and list potential candidate FDCAs which retain their attractor characteristics over change in state.
