Finite State Machine and Matrix Representation for Solving Transition Modeling for Dynamic Programming Solution

Efficient computation of expected values is paramount in scenario analysis and decision-making, especially for problems involving large finite state machines with complex state dependencies and transitions. Traditional approaches re-lying on linear equation systems often fall short under such de-manding conditions. Addressing this critical need, the proposed method integrates finite state machines to model transitions and matrices to manage state properties, delivering a breakthrough in efficiency. The matrix transition model, enhanced with an optimized memory management technique, achieves an average computation time of just 0.179 seconds—over 22 times faster than the strict 4-second time limit set by the problem setter—and consumes only 5.63 MB of memory, a mere 0.36% of the 1536 MB limit. These results underscore the solution’s exceptional capability to not only meet but vastly exceed stringent performance requirements, redefining expectations for large-scale finite state machine calculations.