New methods to generate hard random problem instances have driven progress on algorithms for deduction and constraint satisfaction. Recently Achlioptas et al. (AAAI 2000) introduced a new generator based on Latin squares that creates only satisfiable problems, and so can be used to accurately test incomplete (one sided) solvers. We investigate how this and other generators are biased away from the uniform distribution of satisfiable problems and show how they can be improved by imposing a balance condition. More generally, we show that the generator is one member of a family of related models that generate distributions ranging from ones that are everywhere tractable to ones that exhibit a sharp hardness threshold. We also discuss the critical role of the problem encoding in the performance of both systematic and local search solvers.
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