Ştefan MIRICĂ, A Dynamic programming solution to Bernoulli's brachistochrone problem, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 39 (87), No. 1/4 ...

Discrete decision processes provide a convenient means of problem statement, while monotone sequential decision processes (which are finite automata with a certain cost structure superimposed) ...