Better Complexity Bounds for Cost Register Automata
MFCS(2018)
摘要
Cost register automata (CRAs) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the tropical semiring (ℕ∪{∞},min ,+) can simulate polynomial time computation, proving along the way that a naturally defined width- k circuit value problem over the tropical semiring is -complete. Then the copyless variant of the CRA, requiring that semiring operations be applied to distinct registers, is shown no more powerful than ^1 when the semiring is (ℤ,+,× ) or (Γ^*∪{},max ,concat) . This relates questions left open in recent work on the complexity of CRA-computable functions to long-standing class separation conjectures in complexity theory, such as versus and NC 1 versus GapNC 1 .
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关键词
Computational complexity,Circuit complexity,Cost register automata,Arithmetic circuits,Tropical semiring
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