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...

Full description

Saved in:
Bibliographic Details
Published inTheory of computing systems Vol. 63; no. 3; pp. 367 - 385
Main Authors Allender, Eric, Krebs, Andreas, McKenzie, Pierre
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2019
Springer Nature B.V
Subjects
Automata theory
Complexity theory
Computer Science
Computer simulation
Theory of Computation
Cost register automata
Tropical semiring
Computational complexity
Circuit complexity
Arithmetic circuits
Online AccessGet full text

Cover

More Information
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 .
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-018-9871-4