This paper develops a method for early detection of lean-blow-out (LBO) in combustion systems by extracting low-dimensional features from chemiluminescence time series of optical sensor data. In the proposed method, symbol strings are generated by partitioning the (finite-length) time series to construct a special class of probabilistic finite state automata (PFSA), called D-Markov machines. These PFSA have a deterministic algebraic structure and their states are represented by symbol blocks of length D or less. The states of D-Markov machines are constructed in two steps: (i) state splitting, i.e., the states are split based on their information contents, and (ii) state merging, i.e., two or more states (of possibly different lengths) are merged together to form a new state without any significant loss of their embedded information. The modeling complexity (i.e., the number of states) of a D-Markov machine is observed to be drastically reduced as the combustion system approaches LBO. The prediction of LBO is posed as a pattern classification problem based on different ranges of equivalence ratio of the flame. It is shown that, over a wide range of air-fuel premixing, a generalized D-Markov machine (i.e., with D > 1) performs better than a D-Markov machine with D = 1 as a predictor of LBO.