We present an oracle factorisation algorithm, which in polynomial deterministic time, finds a nontrivial factor of almost all positive integers n based on the knowledge number points certain elliptic curves residue rings modulo n.

We introduce a new automaton on a word p, sequence of letters taken in an alphabet , that we call factor oracle. This automaton is acyclic, recognizes at least the factors of p, has m + 1 states and a linear number of transitions. We give an on-line construction algorithm of the factor oracle. The tight links between this structure and the suux automaton allows us to introduce a second structur...

This paper presents an economic model predictive controller, under the assumption that only measurable signal of plant is cost to be minimized. In order forecast evolution this for a given input trajectory, prediction with NARX structure, so-called oracle, proposed. Sufficient conditions ensure existence such oracle are studied, proving it can derived general nonlinear system if function Morse ...

Whereas the use of distributed ledger technologies has previously been limited to cryptocurrencies, other sectors—such as healthcare, supply chain, and finance—can now benefit from them because bitcoin scripts smart contracts. However, these applications rely on oracles fetch data real world, which cannot reproduce trustless environment provided by blockchain networks. Despite their crucial rol...

We propose a couple of oracle construction methods for quantum pattern matching. in turn show that one the construct can be used with Grover's search algorithm exact and partial matching, deterministically. The other also points to matched indices, but primarily provides means generate Hamming distance between searched all possible sub strings input string, probabilistic way.