TY - GEN
T1 - Better complexity bounds for cost register automata
AU - Allender, Eric
AU - Krebs, Andreas
AU - McKenzie, Pierre
N1 - Publisher Copyright:
© Eric Allender, Andreas Krebs, and Pierre McKenzie; licensed under Creative Commons License CC-BY.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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 U [{∞}, 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 NC1 when the semiring is (z,+,x) or (γ[U{ω}, 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 NC1 versus GapNC1.
AB - 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 U [{∞}, 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 NC1 when the semiring is (z,+,x) or (γ[U{ω}, 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 NC1 versus GapNC1.
KW - Computational complexity
KW - Cost registers
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U2 - 10.4230/LIPIcs.MFCS.2017.24
DO - 10.4230/LIPIcs.MFCS.2017.24
M3 - Conference contribution
AN - SCOPUS:85038442246
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
A2 - Larsen, Kim G.
A2 - Raskin, Jean-Francois
A2 - Bodlaender, Hans L.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
Y2 - 21 August 2017 through 25 August 2017
ER -