This paper presents mathematical models, algorithms, and a software framework for formal languages and systems controlled by Petri nets. The proposed approach integrates formal language theory, Petri-net-based control mechanisms, and parallel execution strategies to analyze the generative and computational properties of formal systems. Mathematical models based on multiset algebra and labeled Petri nets are developed to support step, multistep, and maximal-step execution modes. Experimental results demonstrate that the maximal parallel firing strategy reduces the average derivation-tree depth by approximately 34%, thereby improving the efficiency of state-space exploration and formal analysis. A conflict-resolution mechanism is introduced to eliminate deadlock situations arising from concurrent access to shared resources. The obtained results confirm the effectiveness of the proposed approach in modeling concurrent computational processes and analyzing the expressive power of formal language families.