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Chapter 0: Q9E (page 27)
Write a formal description of the following graph.
The formal description of the graph is:
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Let
contains all size 3 columns of 0s and 1 s. A string of symbols ingives three rows of 0s and 1s. Consider each row to be a binary number and let B=the bottom row of W is the sum of the top two rows}.
For example,
Show that Bis regular.
(Hint: Working with is easier. You may assume the result claimed in Problem 1.31.)
Give an example in the spirit of the recursion theorem of a program in a real programming language (or a reasonable approximation thereof) that prints itself out.
Question: Let Show that S nor S' neither is Turing recognizable.
Let be strings and let L be any language. We say that x and y are distinguishable by L if some string Z exists whereby exactly one of the strings is a member of L ; otherwise, for every string z , we have whenever and we say that are indistinguishable by L. If are indistinguishable by L, we write x 鈮 y. Show thatis an equivalence relation.
Let Show that is decidable.
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