8 papers
A Computation Model with Automatic Functions and Relations as Primitive Operations
Ziyuan Gao, Sanjay Jain, Li Zeyong +2
Prior work of Hartmanis and Simon (Hartmanis and Simon, 1974) and Floyd and Knuth (Floyd and Knuth, 1990) investigated what happens if a device uses primitive steps more natural th…
Ordered Semiautomatic Rings with Applications to Geometry
Ziyuan Gao, Sanjay Jain, Ji Qi +3
The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geome…
Learnability and Positive Equivalence Relations
David Belanger, Ziyuan Gao, Sanjay Jain +2
Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence…
A Faster Exact Algorithm to Count X3SAT Solutions
Gordon Hoi, Sanjay Jain, Frank Stephan
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assig…
A Fast Exponential Time Algorithm for Max Hamming Distance X3SAT
Gordon Hoi, Sanjay Jain, Frank Stephan
X3SAT is the problem of whether one can satisfy a given set of clauses with up to three literals such that in every clause, exactly one literal is true and the others are false. A…
Random Subgroups of Rationals
Ziyuan Gao, Sanjay Jain, Bakhadyr Khoussainov +4
This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup of rationals, two main…