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No,it's actually right. See my post comment answering the same question. It is the circuit models that actually pose a harder challenge, but even if you won't accept my reasonable zero-cost encoding where a misconnected input is interpreted as a constant 0,the cost of validation is still less than even untyped LC.



You state there that "at worst I would need O(n) time" so are you in fact conceding that my claim "It takes non-zero effort to determine whether the code for a Turing machine actually implements a valid Turing machine." was correct?

https://pressron.wordpress.com/2016/08/30/what-we-talk-about...


I gave a natural, reasonable encoding that requires zero validation: every string is a valid TM, and every TM can be easily represented by that encoding and directly executed. However, some may object to the encoding on some grounds, so I said that even the strictest critic would agree to a more complex validation, which is still lower than that of untyped LC. Similarly, I made lenient assumptions about untyped LC (variable shadowing). Without it, you'd need to keep track of every variable that's in scope, so as not to accidentally bind it again. With it, evaluation becomes complex by a bigger factor than a TM becomes under my zero-cost representation.

It's important to understand that encoding is always a tricky subject, because every different encoding requires a different interpreter, and one could ask whether that interpreter is really the "original" TM or "original" LC (of course, there's no argument over huge complexity differences, but slight ones are up for some debate). I think that under very natural, reasonable encodings, the machine models require zero validation; I also think that allowing variable shadowing in LC is reasonable and doesn't completely change the model. It's perfectly OK to disagree with me on this point, but it really doesn't make a difference.

As to providing more detail in the post, well, I don't want to get lost in details that are ultimately inconsequential, and no matter what level of detail you choose, there will always be those who don't find it detailed enough. I prefer the interactive approach of an online discussion.




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