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 …
Blog
[Solved]: Pumping lemma problem – Choosing the right string to pump
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 …
[Solved]: Is a partial function Turing-computable?
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 …
[Solved]: Program synthesis, decidability and the halting problem
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 …
[Solved]: Decremental reachability in a grid graph
Problem Detail: Consider an $n$ by $n$ grid graph. For example, the following. You can of course reach the top left corner from the bottom right. Now consider the graph dynamically with an arbitrary number of edges deleted at each step. Read More …
[Solved]: Synchronizing sequence and Synchronizable DFA
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 …
[Solved]: Name of Bomberman algorithm?
Problem Detail: Last couple of days I’ve been pulling my hair trying to find the name of a bomberman-esque algorithm which finds solutions to the question of where to place a single bomb so as to blow all targets up, either Read More …
[Solved]: Partition an infinite regular language into 2 disjoint infinite regular languages
Problem Detail: Given any infinite regular language $L$, how can I prove that $L$ can be partitioned into 2 disjoint infinite regular languages $L_1, L_2$? That is: $L_1 cup L_2 = L$, $L_1 cap L_2 = varnothing$, and $L_1$ and $L_2$ Read More …
[Solved]: What is the difference between a problem and an algorithm?
Problem Detail: I can say that $x * y$ is a problem, but also I can say that $x * y$ is an algorithm for finding the area of rectangle. I been reading Wikipedia about an algorithm and a problem, but Read More …
[Solved]: Is it allowed to do a binary search with an oracle when proving NP-completeness?
Problem Detail: In http://cs.stackexchange.com/a/45524/28999, they do a binary search using an oracle for an NP-Complete problem. They show that the original problem can be reduced to that NP-Complete problem, implying that the original problem is in NP. Why is that allowed? Read More …
