Προσδιορισμός του ελάχιστου μιας μη γραμμικής συνάρτησης υπό τους όρους μη γραμμικών περιορισμών κατά μήκος καμπυλόγραμμων μονοπατιών αναζήτησης. / Definition of the minimum of a non linear function by using non linear constraines.

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.