Proving Church's Thesis

t) Yuri Gurevich Microsoft Research The talk reflects recent joint work with Nachum Dershowitz [4]. In 1936, Church suggested that the recursive functions, which had been defined by G¨odel earlier that decade, adequately capture the intuitive notion of a computable (“effectively calculable”) numerical function1 [2]. Independently Turing argued that, for strings-to-strings functions, the same goal is achieved by his machines [11]. The modern form of Church’s thesis is due to Church’s student Kleene. It asserts that every computable numerical partial function is partial recursive. (Originally Church spoke of total functions.) Kleene thought that the thesis as unprovable: “Since our original notion of effective calculability. . . is a somewhat vague intuitive one, the thesis cannot be proved” [7]. But he presented evidence in favor of the thesis. By far the strongest argument was Turing’s analysis [11] of “the sorts of operations which a human computer could perform, ...

• Type: Conference
• Year: 2007
• Where: CSR
• Authors: Yuri Gurevich
• Keywords: Church’s Thesis, Computable, CSR 2007, Effective Calculability