Space-time tradeoffs and first order problems in a model of programs

We introduce a model of programs for comparison-based problems. This model gives a measure of space usage and is “uniform”. We first obtain upper and lower bounds on the selection problems which demonstrate the tradeoffs between time and space. We next introduce the class of first order problems and characterize them semantically. A surprisingly simple classification of first order problems into three complexity classes is shown. Finally we extend the first order problems to the weak second order problems and show that these can be solved in polynomial time by programs in our model augmented with push-down stores.

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