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Sorting networks are oblivious sorting algorithms with many practicalapplications and rich theoretical properties. Propositional encodings ofsorting networks are a key tool for proving concrete bounds on the minimumnumber of comparators or depth (number of parallel steps) of sorting networks.In this paper, we present new SAT encodings that reduce the number of variablesand clauses of the sorting constraint of optimality problems. Moreover, theproposed SAT encodings can be applied to a broader class of problems, such asthe search of optimal single-exception sorting networks and $\epsilon-$halvers.We obtain optimality results for single-exception sorting networks on $n \le10$ inputs.

SAT encodings for sorting networks, single-exception sorting networks and $\epsilon-$halvers