Author: ignougroup

Problem Detail: Is there an algebraic characterization of the number of words of a given length in a regular language? Wikipedia states a result somewhat imprecisely: For any regular language $L$ there exist constants $lambda_1,,ldots,,lambda_k$ and polynomials $p_1(x),,ldots,,p_k(x)$ such that for Read More …

Problem Detail: I have the following context-free language: S -> ASa | b A -> aA | a I don’t understand why this is not regular. I first said that it’s generated by the regular expression a+ba+. The following is regular Read More …

Problem Detail: In class, we saw the Miller-Tucker-Zemlin formulation of the Travelling Salesmen Problem (TSP). MTZ is a way of formulating the TSP as an integer linear programming instance. I understand how MTZ works, but I’m confused why MTZ is considered Read More …

Problem Detail: So we can prove that the language say $A = { langle M,w rangle mid text{M is TM that accepts } w^R text{ whenever it accepts } w }$ is undecidable by assuming it is decidable and use that Read More …

Problem Detail: I started reading more and more language research papers. I find it very interesting and a good way to learn more about programming in general. However, there usually comes a section where I always struggle with (take for instance Read More …

Problem Detail: Apparently, for every k-tape Turing machine that runs in time $O(t(n))$, there exists a 1-tape Turing machine that runs in $O(t^2(n))$. I can see how any multi-tape machine $M$ can be simulated by a 1-tape machine $S$. Just have Read More …

Problem Detail: I am having hard time solving the following problem. Are there any languages for which $$ overline{L^*} = (overline{L})^* $$ Assuming $emptyset^* = emptyset$, if I consider $Sigma = {a}$ and L = $Sigma^*$, I get that $L^* = Read More …

Problem Detail: Intro graphics courses usually have a project that asks you to build a ray tracer to render a scene. Many graphics students entering grad school say that they want to work on ray tracing. And yet it seems that Read More …

Problem Detail: My language is the repetition of 0 to a length that’s a power of 2: $L = { 0^k ni k=2^n, n geq 1 }$ I want to know how to prove that this language is not regular. I Read More …

Problem Detail: Initially, Matroids were introduced to generalize the notions of linear independence of a collection of subsets $E$ over some ground set $I$. Certain problems that contain this structure permit greedy algorithms to find optimal solutions. The concept of Greedoids Read More …