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 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

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 can simulate polynomial time computation, proving along the way that a naturally dened 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 the integers, or strings with operations max and 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.Peer reviewe

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 can simulate polynomial time computation, proving along the way that a naturally dened 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 the integers, or strings with operations max and 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.Paper presented at the 42nd International Symposium on Mathematical Foundations of Computer Science, August 21-25, 2017, Aalborg, Denmark. This is the Author’s Original, a longer and more complete version of the paper published in: Larsen, K.G., Bodlaender, H.L., & Raskin, J.-F. (Eds.). (2017). Proceedings from 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Dagstuhl, Germany: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. (Leibniz International Proceedings in Informatics (LIPIcs)). DOI: 10.4230/LIPIcs.MFCS.2017.24.Peer reviewed