Existentially restricted quantified constraint satisfaction

The quantified constraint satisfaction problem (QCSP) is a framework for modelling PSPACE computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In this paper, we introduce and study a new model for investigating QCSP complexity in which the types of constraints given by the existentially quantified variables, is restricted. Our primary technical contribution is the development and application of a general technology for proving positive results on parameterizations of the model, of inclusion in the complexity class coNP.