computation-theory

As far as I know, a Turing machine can be made to execute loops or iterations of instructions encoded on a Tape. This can be done by identifying Line separators and making the Turing machine go back until a specific count of Line separators is reached (that is, inside the loop). But, can a Turing machine also execute a recursive program? Can someone describe various details for such a Turing Machine? I suppose, if recursion can be executed by a Turing machine, the Quicksort can also be performed? If the question is if a Turing Machine can execute a sorting algorithm, the answer is yes, since

Out of these algorithms, I know Alg1 is the fastest, since it is n squared. Next would be Alg4 since it is n cubed, and then Alg2 is probably the slowest since it is 2^n (which is supposed to have a very poor performance). However Alg3 and Alg5 are something I have yet to come across in my reading in terms of speed. How do these two algorithms rank up to the other 3 in terms of which is faster and slower? Thanks for any help. Edit: Now that I think about it, is Alg3 referring to O(n log n)? If the ln inside of it means 'log', then that would make it the fastest. Gumbo The ascending order would

I need a CFG which will generate strings other than palindromes. The solution has been provided and is as below.(Introduction to theory of computation - Sipser) R -> XRX | S S -> aTb | bTa T -> XTX | X | <epsilon> X -> a | b I get the general idea of how this grammar works. It mandates the insertion of a sub-string which has corresponding non-equal alphabets on its either half, through the production S -> aTb | bTa , thus ensuring that a palindrome could never be generated. I will write down the semantics of the first two productions as I have understood it, S generates strings which cannot be

Can anyone outline for me an algorithm that can convert any given regex into an equivalent set of CFG rules? I know how to tackle the elementary stuff such as (a|b)*: S -> a A S -> a B S -> b A S -> b B A -> a A A -> a B A -> epsilon B -> b A B -> b B B -> epsilon S -> epsilon (end of string) However, I'm having some problem formalizing it into a proper algorithm especially with more complex expressions that can have many nested operations. If you are just talking about regular expressions from a theoretical point of view, there are these three constructs: ab # concatenation a|b # alternation