Better Complexity Bounds for Cost Register Automata
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 po...
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Published in | Theory of computing systems Vol. 63; no. 3; pp. 367 - 385 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.04.2019
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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
P
-complete. Then the copyless variant of the CRA, requiring that semiring operations be applied to distinct registers, is shown no more powerful than
NC
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
NC
versus
P
and NC
1
versus GapNC
1
. |
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ISSN: | 1432-4350 1433-0490 |
DOI: | 10.1007/s00224-018-9871-4 |