eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-01
24:1
24:14
10.4230/LIPIcs.MFCS.2017.24
article
Better Complexity Bounds for Cost Register Automata
Allender, Eric
Krebs, Andreas
McKenzie, Pierre
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 {infinity},\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,+,x) or (Gamma^*,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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol083-mfcs2017/LIPIcs.MFCS.2017.24/LIPIcs.MFCS.2017.24.pdf
computational complexity
cost registers