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We study Turing machines over sets with atoms, also known as nominal sets. Our main result is that deterministic machines are weaker than nondeterministic ones; in particular, P6=NP in sets with atoms. Our main construction is closely related to the Cai-F¨urer-Immerman graphs used in descriptive complexity theory.
The paper presents an algorithm of the exact symbolic network function analysis that deals with circuits with any size. The only condition is to decompose the whole circuit into smaller sub-circuits. The decomposition is the multi-level hierarchical one. What is more, the calculation for each level can be done only once and the partial results can be reused any time. A higher level subcircuit does...
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