The Utilization of Single-Counter Systems Featuring Final Terminals with Non-Zero Counter Values

Hidden probabilistic one counter models (HPOCA) that are a specific model where spotting between hidden Markov models (HMMs) and probabilistic context-free grammars (PCFGs) which is a subclass of probabilistic pushdown automata contains only one stack symbol In this study, we propose a new model in which the final terminal counter value is different from zero. With this proposed model, we enhance the existing HPOCA, making it more complex. Consequently, as there will be a greater number of paths to reach the final terminal, we also evaluate the probability of reaching the target through alternative routes based on the given observation sequence. It makes the model more expressive than default HPOCA due to providing alternative final terminals. However, the inference of the final counter value could easily go to an infinite number without any threshold. A boundary is applied to prevent the occurrence of this unexpected condition. By applying this threshold value, we ensured that the computational complexity of the model is quadratic rather than cubic.