An algorithmic approximation of the infimum reachability probability for Probabilistic Finite Automata

Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with the known result that the approximation problem is undecidable if we consider the supremum instead of the infimum. Since we study the probability of reaching a set of states, instead of the probability of ending in an accepting state, our work is more related to model checking than to formal languages.

💡 Research Summary

The paper addresses the quantitative verification problem for Probabilistic Finite Automata (PFA) by focusing on the infimum reachability probability rather than the more commonly studied supremum (maximum) acceptance probability. Given a PFA A = (Q, Σ, δ, q₀), a set of target states S ⊆ Q, and an error tolerance ε > 0, the authors present a constructive algorithm that computes a value p such that
 Inf ≤ p ≤ Inf + ε,
where Inf = inf_{w∈Σ^ω} Pr_A^w