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- W2771131742 abstract "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 $(mathbb {N}cup {infty },min ,+)$ can simulate polynomial time computation, proving along the way that a naturally defined width-k circuit value problem over the tropical semiring is $textsf {P}$ -complete. Then the copyless variant of the CRA, requiring that semiring operations be applied to distinct registers, is shown no more powerful than $textsf {NC}^{1}$ when the semiring is $(mathbb {Z},+,times )$ or $({Gamma }^{*}cup {bot },max ,text {concat})$ . 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 $textsf {NC}$ versus $textsf {P}$ and NC1 versus GapNC1." @default.
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- W2771131742 date "2018-06-13" @default.
- W2771131742 modified "2023-10-18" @default.
- W2771131742 title "Better Complexity Bounds for Cost Register Automata" @default.
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- W2771131742 doi "https://doi.org/10.1007/s00224-018-9871-4" @default.
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