On the parity complexity measures of Boolean functions

The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decision trees, as well as with communication complexity.