Author: ignougroup

Problem Detail: I am trying to prove problem 1.59 in Sipser’s book: Introduction to the theory of computation , 2nd Edition. Let $M=(Q,Sigma,delta,q_0,A)$ be a DFA and let $q’$ be a state of $M$ called its “home”. A Synchronizing sequence for Read More …

Problem Detail: I was reading an answer to a recent question, and sort of a strange, ephemeral thought came to mind. My asking this might betray either that my theory chops are seriously lacking (mostly true) or that it’s just too Read More …

Problem Detail: From my understanding for a function to be considered Turing-computable the Turing machine which computes it must terminate for all inputs (according to this http://planetmath.org/turingcomputable and various other sources I’ve read). But then doesn’t this mean that all partial Read More …

Problem Detail: I have a problem finding the right string to pump for the following language: $$L_1 = {a^{p+q}b^rc^sd^{q+r}e^s mid p, q, r, s ge 0}$$ Which string should I choose to pump? The problem is that I don’t know how Read More …

Problem Detail: In Type Theory if one allows Type to be a member of itself, it makes the theory inconsistent. I understand it by analogy to Russel’s paradox in Set Theory, but would prefer to see it done in Type Theory. Read More …

Problem Detail: I am kind of unsure about a reduction between two problems. Here are the two problems: PARTITION: Instance: A finite set of n positive integers $S= {a_1,a_2,…a_n}$. Question: Can the set $S$ be partitioned into two subsets $S_1$,$S_2$, s.t. Read More …

Problem Detail: Lets say $G$ is complete undirected graph with a set of edges coloured either black or red. The problem is to find an algorithm answering if it is possible to remove a subset of nodes from $G$ in a Read More …

Problem Detail: Throughout the subject of reductions, I was wondering: If we take $L_1 = Sigma^* $ and $L_2 = emptyset$, is $L_1 leq L_2$? is $L_2 leq L_1$? What I mean is, Is there some sort of reduction between any Read More …

Problem Detail: I understand without memoization it is going to be $O(3^{max,{m,n}})$ because every call results in extra three calls: thus we end up having a call tree with three children for each node, with height $max,{m,n}$, m and n being Read More …