Problem Detail: I am going to teach a course in set theory for software engineering students. I am going to talk in this course about: ordinal numbers, partial orders, well ordering, generic filters and maybe some cardinal invariants (such as $mathfrak Read More …
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[Solved]: alphabet of a single tape turing machine that simulates a multitape TM
Problem Detail: First of all sorry, if this question already exists, in that case, pointing to the right direction will be appreciated. Secondly, sorry, if the question is below the expected level of Niveau, but all help appreciated. In the textbook Read More …
[Solved]: How does a turing machine with doubly infinite tape simulate a normal-taped turing machine?
Problem Detail: The intuition is that on any input, we can write a symbol like $#$ on the left that tells the machine to not move past this symbol. However, I’m running into problems trying to show this using the formal Read More …
[Solved]: Is linear-time reduction symmetric?
Problem Detail: By reduction I mean the following: Problem X linear reduces to problem Y if X can be solved with: a) Linear number of standard computational steps. b) Constant calls to subroutine for Y. If a problem X reduces to Read More …
[Solved]: What is the TAK function for?
Problem Detail: We covered this in class today. I understand the mechanics of it, but aside from being a nice example of recursion does it serve any purpose? Searching the web reveals lots of pages with the formula and it’s implementation Read More …
[Solved]: Description of resolution algorithm as it applies to SAT
Problem Detail: SAT [5] can be solved with resolution definitively, i.e. if the formula has a true assignment, resolution can find it, and if it cant be satisfied, resolution can show that no assignment exists (at least in exponential time/space.). [4] Read More …
[Solved]: Does every DFA contain a loop?
Problem Detail: Is there a rule that either every DFA contains or not, a loop(cycle in graph terminology)? I do not seem to be able to generalize this idea in either direction. Also if either of these is true, can we Read More …
[Solved]: Solving recurrence with logarithm squared $T(n)=2T(n/2) + n log^2n$
Problem Detail: $T(n)=2T(n/2) + nlog^2(n)$. If I try to substitute $m = log(n)$ I end up with $T(2^m)=2 T(2^{m-1}) + 2^mlog^{2}(2^m)$. Which isn’t helpful to me. Any clues? PS. hope this isn’t too localized. I specified that the problem was a Read More …
[Solved]: Why is $n log log n$ not tightly bounded by $n$?
Problem Detail: I don’t understand why $n log log n $ is not $Theta (n)$. Suppose we give $n$ a value of $10,000$. Then $n log log n$ is $6020.6$. So isn’t $n log log n$ upper- and lower-bounded by $n$, Read More …
[Solved]: Difference between Dominant strategy and Winning Strategy
Problem Detail: I am a little bit confused by the definition of dominant strategy and winning strategy, what’s the difference between them. Following are the definitions taken from wikipedia, below every definition I added some thoughts. If you fell that my Read More …
