Equivalence of Continuous Alphabet Hidden Markov Models

Hidden Markov Models (HMM) are often natural models for probabilistic events where the underlying mechanism is not directly observable. Furthermore, HMMs where the observable signal belongs to the set of real numbers are useful models for applications like speech recognition technology. Equivalence of two HMMs where the observable signal falls in a finite set is a classical problem dating back to the 70s and is known to be decidable in polynomial time, but equivalence of HMMs with continuous signals was not studied. In this talk I will explain how to reduce decidability of continuous signal chains to decidability of finite signal chains and give this reduction algorithm.

Based on ongoing, unpublished work.