Most statistical parsers have used the grammar induction approach, in which a stochastic grammar is induced from a treebank. An alternative approach is to induce a controller for a given parsing automaton. Such controllers may be stochastic; here, we focus on greedy controllers, which result in deterministic parsers. We use decision trees to learn the controllers. The resulting parsers are surprisingly accurate and robust, considering their speed and simplicity. They are almost as fast as current part-ofspeech taggers, and considerably more accurate than a basic unlexicalized PCFG parser. We also describe Markov parsing models, a general framework for parser modeling and control, of which the parsers reported here are a special case.