Abstract
⊕ L is the class of languages acceptable by logarithmic space bounded Turing machines that work nondeterministically and are equipped with parity-acceptance. Several natural problems are shown to be complete for ⊕ L under NC 1-reductions. A consequence is that ⊕ L is the ▪ 2-analogon of Cook's class DET, the class of problems NC 1-reducible to the computation of determinants over ▪.
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