Problem Detail: I’m having trouble wrapping my head around the problems PRIME, COMPOSITE, FACTOR and how they’re related in terms of complexity. I understand that PRIME has been shown to be in $P$ by the AKS primality test, and I believe Read More …
Category: Uncategorized
[Solved]: Which fixpoint is Haskell list type?
Problem Detail: Let’s say that lists are defined as List a = Nil | Cons a (List a) Then, in Haskell is List x the greatest or least fixpoint? I’m asking because the lfp should exclude infinite lists (but you can Read More …
[Solved]: Language to Construct Finite State Transducer
Problem Detail: I am attempting to write a Finite State Transducer module in OCaml, because I think it’s a good exercise, which is because I have been teaching myself Natural Language Processing. You typically construct finite automata using regular expressions, for Read More …
[Solved]: Structural induction over list
Problem Detail: I want to prove that unique(reverse(L)) = reverse(unique(L)) where L is a List. List has the following constructors: [] : -> List [e] : Element -> List cons(e, L) : Element x List -> List I defined unique and Read More …
[Solved]: How to Study Space Complexity
Problem Detail: I am working through Sipser, and I am trying to understand some of the algorithms described in Space Complexity, but I am having a hard time understanding the presentation of the material (especially Savitch’s theorem). I have a very Read More …
[Solved]: Space(n) not closed under Karp reductions – what about NTime(n)?
Problem Detail: In the book on complexity by Arora and Barak, there is an exercise to show $Space(n)neq NP$, the proof of which goes by showing that $NP$ is closed under Karp reductions, while $Space(n)$ isn’t. To show that $Space(n)$ isn’t Read More …
[Solved]: Relationship of algorithm complexity and automata class
Problem Detail: I have been unable to find a graph depicting or text answering the following question: Is there a direct relationship between the complexity of an algorithm (such as best / worst case of quick sort), and class of automata Read More …
[Solved]: Visualization of Lamport’s three-dimensional “space-time diagram” with introduced “tick lines”
Problem Detail: In the third page (the third paragraph in the right column) of the paper “Time, Clocks, and the Ordering of Events in a Distributed System” by Leslie Lamport, it says that The reader may find it helpful to visualize Read More …
[Solved]: Mapping reducibility vs. Turing reducibility
Problem Detail: Let $A$ and $B$ be two languages. If $A le_{m} B$ ( reducible by mapping ) then I know that if $B$ is decidable so is $A$ and if $B$ is recognizable so is $A$. And if $A le_{T} Read More …
[Solved]: No need to rename a free variable in substitution?
Problem Detail: I wonder if the following two substitutions are correct: $$(x,y)[x:=y] = (y,y)$$ $$ lambda y. (x,y) [x:=y] = lambda z.(y,z)$$ They are what I understand from http://en.wikipedia.org/wiki/Lambda_calculus#Substitution. Although I can follow the rules there mechanically, I wonder why there Read More …
