339,317 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Challenges in computational lower bounds
We draw two incomplete, biased maps of challenges in computational complexity
lower bounds
Logics of Finite Hankel Rank
We discuss the Feferman-Vaught Theorem in the setting of abstract model
theory for finite structures. We look at sum-like and product-like binary
operations on finite structures and their Hankel matrices. We show the
connection between Hankel matrices and the Feferman-Vaught Theorem. The largest
logic known to satisfy a Feferman-Vaught Theorem for product-like operations is
CFOL, first order logic with modular counting quantifiers. For sum-like
operations it is CMSOL, the corresponding monadic second order logic. We
discuss whether there are maximal logics satisfying Feferman-Vaught Theorems
for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th
birthday. The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-23534-9_1
Discrete-Query Quantum Algorithm for NAND Trees
This is a comment on the article âA Quantum Algorithm for the Hamiltonian NAND Treeâ by Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, Theory of Computing 4 (2008) 169--190. That paper gave a quantum algorithm for evaluating NAND trees with running time O(âN) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using N^[1/2 + o(1)] queries in the conventional (discrete) quantum query model
- âŠ