Problem Detail: I have a field in my data store which must take exactly 180 bits of information. Some users will choose to make this data encrypted, some won’t, so some of those 180 bit fields will be ciphertext some will Read More …
Category: Uncategorized
[Solved]: Questions about amortised analysis
Problem Detail: As a preperation of an exam about algorithms and complexity, I am currently solving old exercises. One concept I have already been struggling with when I encountered it for the first time is the concept of amortised analysis. What Read More …
[Solved]: Smallest DFA that accepts given strings and rejects other given strings
Problem Detail: Given two sets $A,B$ of strings over alphabet $Sigma$, can we compute the smallest deterministic finite-state automaton (DFA) $M$ such that $A subseteq L(M)$ and $L(M) subseteq Sigma^*setminus B$? In other words, $A$ represents a set of positive examples. Read More …
[Solved]: Non intersecting paths in a graph
Problem Detail: I’m trying to come up with a good algorithm for the following decision problem: Let $G=(V,A)$ be a directed graph and let $s,t in V$. Are there at-least 2 non-intersecting paths from $s$ to $t$? By non-intersecting I mean Read More …
[Solved]: Turing Machine Decidable: What right does the definition have to say what’s not in language L?
Problem Detail: I’m having trouble understanding the definition of Turing Decidable. The definition goes something like this: TM M decides language L iff the strings in L put M into the Accept state and the strings NOT IN L put M Read More …
[Solved]: Converting Regular expression to DFA by building syntax tree
Problem Detail: There is a way to convert regular expression to DFA (deterministic finite automata) which is to build a syntax tree and then compute first pos, last pos, follow pos, and then use a Transition technique to build DFA for Read More …
[Solved]: Weighted subset sum problem
Problem Detail: Given an integer sequence ${ a_1, a_2, ldots, a_N }$ that has length $N$ and a fixed integer $Mleq N$, the problem is to find a subset $A ={i_1, dots, i_M} subseteq [N]$ with $1 leq i_1 lt i_1 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]: 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]: Can we prove that all CFLs can be recognized by a Turing Machine in polynomial time?
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 …
