Complexity of solvable cases of the decision problem for the predicate calculus

We analyze the computational complexity of determining whether F is satisfiable when F is a formula of the classical predicate calculus which obeys certain syntactic restrictions. For example, for the monadic predicate calculus and the Gödel or ∃ ... ∃∀∀∃ ... ∃ prefix class we obtain lower and upper nondeterministic time bounds of the form cn/log n. The main tool in in these proofs is a finite version of Wang's domino problem, about which we present an interesting open question.