Editing 1266: Halting Problem
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From a '''mathematical''' point of view, this is not true: a Turing machine will never have a hardware failure because it's not a physical machine. It's a theoretical construct, and it's '''defined''' mathematically, independent of any physical hardware. Similarly, ⅓ + ⅓ + ⅓ = 1 no matter what any physical hardware you are computing it on claims. | From a '''mathematical''' point of view, this is not true: a Turing machine will never have a hardware failure because it's not a physical machine. It's a theoretical construct, and it's '''defined''' mathematically, independent of any physical hardware. Similarly, ⅓ + ⅓ + ⅓ = 1 no matter what any physical hardware you are computing it on claims. | ||
− | Another interpretation of [[Randall]]'s code is that | + | Another interpretation of [[Randall]]'s code is that the Program in the parentheses is actually being run whenever his function is called, as is consistent with some programming constructs. In this case, the function would wait until the program finishes and exits before returning "True". Therefore, [[Randall]]'s function is mathematically accurate. It does not solve the problem though, as it simply shifts the question to whether the function itself will ever halt. |
From a '''practical''' point of view, there are of course times that a programmer would want to return "false", since some programs can be mathematically shown to run forever. | From a '''practical''' point of view, there are of course times that a programmer would want to return "false", since some programs can be mathematically shown to run forever. |