This result suggests that there is a close connection between problems which can be decided using unbounded time but a feasible amount of memory space and those which could be solved if we were able to answer certain kinds of existential or universal queries in a single step using a bounded number of alternations between the two kinds of queries. This observation can be used to give an alternative characterization of several of the complexity classes we have considered. Recall, for instance, that \(\textbf{NP}\) can be informally characterized as the set of problems \(X\) for which membership can be established by providing a certificate of the appropriate sort – e.g. \(\phi \in \sc{SAT}\) can be established by exhibiting a satisfying valuation. Similarly, \(\textbf{coNP}\) can be similarly characterized as the set of problems for which non-membership can be established by the existence of such a certificate – e.g. \(\phi\ \not\in \sc{VALID}\) can also be established by exhibiting a satisfying valuation.