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 …
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[Solved]: Quadratic residue and integer factoring
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 …
[Solved]: What CS Textbooks should I buy?
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 …
[Solved]: What’s the real difference between throughput and capacity of a network cable?
Problem Detail: I was preparing a presentation in work on GPON & other optical network technologies using documentation provided by a supplier, and the claim it made was “GPON networks have a capacity of up to 100Tbps”. Instantly that looked odd Read More …
[Solved]: What happens if we expand the alphabet of a given Turing Machine?
Problem Detail: If we expanded the alphabet Sigma = { 0, 1, u, > } to Sigma’ = { 0, 1, 2, u, > }. How would the table change? We’re just learning about Turing Machines in class and I’m Read More …
[Solved]: Describe in English the pattern in the following regular expressions
Problem Detail: Describe (in English phrases) the languages associated with the following regular expression. it says to be as simple as possible #1 (x (yyy + x)*)* #2 (c (cc)*d(dd)*)* for number 1 I got all words in which when y Read More …
[Solved]: What is the name of this logistic variant of TSP?
Problem Detail: I have a logistic problem that can be seen as a variant of $text{TSP}$. It is so natural, I’m sure it has been studied in Operations research or something similar. Here’s one way of looking at the problem. I Read More …
[Solved]: Space complexity of directed and undirected graph
Problem Detail: I have started reading graph theory from Introduction to Algorithm. The author starts by saying that if the graph is dense then: $$|E|text{ close to }|V|^2$$ else if the graph is sparse then: $$|E|text{ is much less than }|V^2|$$ Read More …
[Solved]: Connection between NAND gates and Turing completeness
Problem Detail: I know that NAND gates can be used to create circuits that implement every truth table, and modern computers are built up of NAND gates. What is the theoretical link between NAND gates and Turing completeness? It seems to Read More …
[Solved]: How can I show that the Cook-Levin theorem does not relativize?
Problem Detail: The following is an exercise which I am stuck at ( source: Sanjeev Arora and Boaz Barak; its not homework ) : Show that there is an oracle $A$ and a language $L in NP^A$ such that $L$ is Read More …
