8 citations · 19 across the 40 of their papers we have counts for
40 papers
Why the classes P and NP are not well-defined finitarily
Bhupinder Singh Anand
We distinguish finitarily between algorithmic verifiability, and algorithmic computability, to show that Goedel's 'formally' unprovable, but 'numeral-wise' provable, arithmetical p…
A pictorial proof of the Four Colour Theorem
Bhupinder Singh Anand
We give a pictorial proof that transparently illustrates why four colours suffce to chromatically differentiate any set of contiguous, simply connected and bounded, planar spaces;…
A density-based approach for non-heuristic approximations of prime counting functions
Bhupinder Singh Anand
All the known approximations of the number of primes pi(n) not exceeding any given integer n are derived from real-valued functions that are asymptotic to pi(x), such as x/log x, L…
A case for weakening the Church-Turing Thesis
Bhupinder Singh Anand
We conclude from Goedel's Theorem VII of his seminal 1931 paper that every recursive function f(x_{1}, x_{2}) is representable in the first-order Peano Arithmetic PA by a formula […
Some consequences of interpreting the associated logic of the first-order Peano Arithmetic PA finitarily
Bhupinder Singh Anand
We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Pe…
A simple finitary proof of Goodstein's Theorem
Bhupinder Singh Anand
We assumed that, for every natural number k, there is a natural number u such that the (k-1)th term of G(u) is k^k, and that G(u) terminates finitely. It immediately follows that e…