Problem Detail: This question came up while a group of students at my school were studying for our qualifying exams. The question on an old exam was, Consider the following six classes of languages: Context free (CFL), Regular(REG), P, NP, Recursive(R), Read More …
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[Solved]: Are context-free languages in $a^*b^*$ closed under complement?
Problem Detail: The context-free languages are not closed under complement, we know that. As far as I understand, context-free languages that are a subset of $a^*b^*$ for some letters $a,b$ are closed under complement(!?) Here is my argument. Each CF language Read More …
[Solved]: Removing identical variables in CFG Unit Productions
Problem Detail: Productions of the form A-> A are removed immediately, but what if the production is of the form A -> AA? example: A -> AA | a Asked By : Sebastien Answered By : Deepu In you example the production A->AA Read More …
[Solved]: Real world applications for Steiner Tree Problem?
Problem Detail: Are there real-world applications of the Steiner Tree Problem (STP)? I understand that VSLI chip design is a good application of the STP. Are there any other examples of real world problems that people can suggest of that could Read More …
[Solved]: Solution to recurrence $T(n) = T(n/2) + n^2$
Problem Detail: I am getting confused with the solution to this recurrence – $T(n) = T(n/2) + n^2$ Recursion tree – T(n) Height lg n + 1 | T(n/2) | T(n/4) So it turns out to be – $T(n) = n^2(1 Read More …
[Solved]: Why are all problems in FPTAS also in FPT?
Problem Detail: According to the Wikipedia article on polynomial-time approximation schemes: All problems in FPTAS are fixed-parameter tractable. This result surprises me – these classes seem to be totally different from one another. FPTAS characterizes problems by how easy they are Read More …
[Solved]: Are two non-Turing-recognizable languages closed under union?
Problem Detail: If I have two languages that aren’t Turing-recognizable, is the union between them always not T-recognizable? Why? Asked By : RobotMan Answered By : jmite No, sometimes you can recognize their union. As an example, take a language where it and Read More …
[Solved]: ML function of type ‘a -> ‘b
Problem Detail: Our professor asked us to think of a function in OCaml that has the type ‘a -> ‘b i.e. a function of one argument that could be anything, and that can return a different anything. I thought of using Read More …
[Solved]: Infer number of comets, based upon observations of their periodic visits to Earth
Problem Detail: Can we algorithmically infer the number of comets that orbit the Earth, based upon periodic observations of them, if we cannot tell the comets apart? In more detail: The problem There is an unknown, fixed number of comets, numComets Read More …
[Solved]: Complexity of multiplication
Problem Detail: I’ve been reading around the area of complexity and arithmetic operations using logic gates; one thing that is confusing me is that begin{equation} Theta (n^{2}) end{equation} is quoted as being the complexity for multiplication for iterative adition. But addition Read More …
