Author: ignougroup

Problem Detail: I am preparing to graduate high school. Although I do not intend to study computer science in college, I feel like it might be useful to familiarize myself with the theoretical CS concepts taught in academia (eg. algorithms, structures, Read More …

Problem Detail: I often read that deciding whether or not a number $r$ is a quadratic residue modulo $n$ is an interesting (and hard) problem from number theory (especially if $n$ is not prime). I am looking at the following special Read More …

Problem Detail: There are two context-sensitive languages, $L_1$ and $L_2$. Which of the following statements about them are decidable respectively undecidable? $L_1 = emptyset$ $L_1 = Sigma^*$ $L_1 cap L_2 = emptyset$ $overline{L_1}$ is also a context-sensitive language. $L_1 = L_2$ Read More …

Problem Detail: I see structural induction the usual way for proving an algorithm’s termination property, but it’s not that easy to prove by means of induction on a tree algorithm. Now I am struggling on proving that the pre-order tree traversal Read More …

Problem Detail: I’m given this problem: Consider the following closest-point heuristic for building an approximate traveling-salesman tour. Begin with a trivial cycle consisting of a single arbitrarily chosen vertex. At each step, identify the vertex u that is not on the Read More …

Problem Detail: I was reading Wikipedia’s entry on Kolmogorov Complexity (thanks to this question), which states: It can be shown that the Kolmogorov complexity of any string cannot be more than a few bytes larger than the length of the string Read More …

Problem Detail: Given is the definition of a general problem: ${ langle M, Srangle mid M text{ is a } TM, L_M in S}$. In words: Given a TM M, does M decide a language that is an element of the Read More …

Problem Detail: In my text book it is mentioned that: $emptyset^*={epsilon}$ where $emptyset$ is an empty language. However, we know that $L cdot emptyset = emptyset$, where $L$ is any Language. I am not able to intuitively grasp this concept because Read More …

Problem Detail: I know that we can have 0 accepting states in a DFA, it would just recognize the empty language. What about the case of all states being accepting? Would that mean it would recognize all of the strings in Read More …

Problem Detail: I am stuck with understanding the transformation of final-state acceptance automaton into empty-stack acceptance automaton. From everywhere that I’ve read, it always says introduce a new start state with a new start stack symbol, and another state after the Read More …