A research proposal is another kind of a complicated academic writing you may be asked to complete pursuing a degree. It differs greatly from any other dissertation or thesis sample, as it is a practical proposal on some scientific investigation. It may even be of greater importance to your academia than any other paper you have submitted before. The tricky part in writing your research proposal paper is that it has to be 100% unique and original. No one will analyze a partially plagiarized research proposal, as it is supposed to promote a good start to your future career. Thus, you have to make sure you paper is grammatically flawless, well structured, and plagiarism free.
The word 'efficiently' here means up to polynomial-time reductions . This thesis was originally called Computational Complexity-Theoretic Church–Turing Thesis by Ethan Bernstein and Umesh Vazirani (1997). The Complexity-Theoretic Church–Turing Thesis, then, posits that all 'reasonable' models of computation yield the same class of problems that can be computed in polynomial time. Assuming the conjecture that probabilistic polynomial time ( BPP ) equals deterministic polynomial time ( P ), the word 'probabilistic' is optional in the Complexity-Theoretic Church–Turing Thesis. A similar thesis, called the Invariance Thesis , was introduced by Cees F. Slot and Peter van Emde Boas. It states: "Reasonable" machines can simulate each other within a polynomially bounded overhead in time and a constant-factor overhead in space .  The thesis originally appeared in a paper at STOC '84, which was the first paper to show that polynomial-time overhead and constant-space overhead could be simultaneously achieved for a simulation of a Random Access Machine on a Turing machine.