The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically non-elementary worst-case complexity. The implementation has matured over a period of six years. Compared to the first naive version, the present tool is faster by several orders of magnitude. This speedup is obtained from many different contributions working on all levels of the compilation and execution of formulas. We present a selection of implementation "secrets" that have been discovered and tested over the years, including formula reductions, DAGification, guided tree automata, three-valued logic, eager minimization, BDD-based automata representations, and cache-conscious data structures. We describe these techniques and quantify their respective effects by experimenting with separate versions of the MONA tool that in turn omit each of them.

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We describe Qubos (QUantified BOolean Solver), a decision procedure for quantified Boolean logic. The procedure is based on nonclausal simplification techniques that reduce formulae to a propositional clausal form after which o#-the-shelf satisfiability solvers can be employed. We show that there are domains exhibiting structure for which this procedure is very e#ective and we report on experimental results.

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