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. 
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