Data Structures and Algorithms

   

Nonuniform Linear Depth Circuits Decide Everything

Authors: Luowen Qian

In this work, we introduce the nonuniform complexity class LD, which stands for linear depth circuit. We also prove that LD = ALL, which is the complexity class that contains all decision languages, and therefore resolving all questions on this new complexity class. No further research is needed [Mun20]. In principle, this shows that anything can be computed via circuits in linear time, despite with (possibly undecidable) pre-computation and very inefficient advice, however, we note that exponential sized advice suffices to achieve ALL.

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[v1] 2020-03-31 18:53:56

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