From Logic to Physics: How the Meaning of Computation Changed over Time

The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of …nite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. Finally, the robustness of the boundary between polynomial and exponential time complexity is considered in connection with quantum computers and quantum information theory. Key words: Church-Turing thesis, hyper-computation, quantum computers 1 The Church-Turing thesis and the meaning of ‘computable function’ The common formulation of the Church-Turing thesis runs as follows: Every computable function is computable ...

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Itamar Pitowsky
• Keywords: Church-Turing Thesis, CIE 2007, Quantum Computers, Turing Machine