Problem Detail: I’m a beginner in learning about computational complexity and this has stumped me. I’ve read that by the time hierarchy theorem, it’s known that EXP-complete problems are not in P. (Wikipedia) It makes absolute sense intuitively that this is Read More …
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[Solved]: Attempt to write a function with cubed log runtime complexity $O(log^3 n)$
Problem Detail: I’m learning Data Structures and Algorithms now, I have a practical question that asked to write a function with O(log3n), which means log(n)*log(n)*log(n). public void run(int n) { for (int i = 1; i < n; i *= 2) Read More …
[Solved]: Definition of “K-fairness” with respect to concurrency?
Problem Detail: There are definitions of Absolute, Strong and Weak Fairness available across the internet, but I cannot find a definition of “K-Fairness” property for critical section algorithms (also algorithms that satisfy a 1-fairness or 3-fairness property). Does this actually exist Read More …
[Solved]: NP-complete reductions
Problem Detail: I’ve read that “Every problem in NP can be reduced to every NP-complete problem”. My question is on the choice of the word “reduce”. If I were to “reduce” a polynomial problem in NP to an exponential problem in Read More …
[Solved]: Can we understand SVM without knowledge of Machine Learning
Problem Detail: I was told by my adviser (future one) to look into libsvm library or any other and try to get familiar with it.. to work on a programming project (on Machine Learning) (will start in a month). my background: Read More …
[Solved]: Depth-2 circuits with OR and MOD gates are not universal?
Problem Detail: It is well-known that every boolean function $f:{0,1}^nto {0,1}$ can be realized using a boolean circuit of depth 2 (over the variables, their negation and constant values) containing AND gates in the first level and one single OR gate Read More …
[Solved]: If one shows that UNIQUE k-SAT is in P, does it imply P=NP?
Problem Detail: Valiant & Vazirani proved SAT is reducible to UNIQUE SAT under randomized probabilistic reductions in polynomial time. Calabro et al. showed that UNIQUE k-SAT is as hard as k-SAT. Now the question is, if someone shows s that UNIQUE Read More …
[Solved]: Can a language have $Sigma^{*}$ as its syntactic monoid?
Problem Detail: As per the title I was wondering if it’s possible for a language $L subseteq Sigma^{*}$ to have $Sigma^{*}$ as its syntactic monoid and if so could one give an example of such a language? I first thought that Read More …
[Solved]: Which theoretical parallel model is closest to CUDA?
Problem Detail: Which theoretical parallel model is closest to CUDA/OpenCL programming model? For example, it fits at some degree to the generic Parallel Random Access Machine (PRAM) model. However, that is too generic, since it makes abstraction of various memory access Read More …
[Solved]: Some slight confusion with the UNTIL operator in CTL (e.g. a U b)
Problem Detail: I’ve sketched a very small transition system in paint that I’ll use as an example. I want to see if $A(aUb)$ holds for this transition system. From my understanding, this CTL formula is asking if ALL paths satisfy $aUb$. Read More …
