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- 2"A programming language is turing complete if you can do any calculation with it." That's the Church-Turing thesis, not what makes a language Turing-complete.user36409– user364092014-05-20 13:47:13 +00:00Commented May 20, 2014 at 13:47
- @Rhymoid So you mean nothing is turing complete unless you can make an interpreter? Ie. lambda calculus is not turing complete even if it's turing equalent?Sylwester– Sylwester2014-05-20 15:58:15 +00:00Commented May 20, 2014 at 15:58
- 1I'm still looking for an authoritative definition of the terms Turing-equivalent and Turing-complete (and Turing-powerful). I've already seen too many cases, from people on message boards to researchers in their own friggin' papers, who interpret these terms differently.user36409– user364092014-05-20 16:12:14 +00:00Commented May 20, 2014 at 16:12
- Anyway, I interpret 'Turing-complete' as being simulation equivalent to a Universal Turing Machine (UTM; which, in turn, is capable of simulating any Turing machine -- hence 'universal'). In Turing's paper from 1936, where he introduced his machines, he defined the notion of a UTM, and gave a sketch of a proof that UTMs are simulation equivalent to Church's lambda calculus. By doing so, he proved that they had the same computational power. The Church-Turing thesis asserts, put simply, that "that's all the computational power you'll ever get".user36409– user364092014-05-20 16:19:01 +00:00Commented May 20, 2014 at 16:19
- It has two formal definitions for Turing completeness page of Wikipedia. One requires I/O the other doesn't. The one that doesn't say that a machine is turing complete if it can calculate every Turing-computable function. That puts lambda calculus back to being turing complete since you can easily make a equalent program in lambda calculus that calculates the same as any turing machine programs.Sylwester– Sylwester2014-05-20 16:19:30 +00:00Commented May 20, 2014 at 16:19
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