Problem Detail: Assume the halting problem was decidable. Is then every recursively enumerable languagerecursive? Asked By : umang Answered By : Peter While we know for sure that the halting problem is (and always will be) undecidable by a Turing machine, we can Read More …
Category: Uncategorized
[Solved]: Logical Reduction
Problem Detail: Reducing one computable problem to another by providing an algorithm which transforms an instance of one problem to one of the other (and limiting the time or space of that algorithm) is clear to me. However, I fail to Read More …
[Solved]: Is the set-partition problem polynomial time reducible to the subset-sum problem?
Problem Detail: There are many solutions on the web showing that the subset-sum problem is polynomial time reducible to the set-partition problem. However, during my search, I came across the following powerpoint presentation (slide 12), where it says that the inverse Read More …
[Solved]: How can an extended linearizable history G be equivalent to sequential history S?
Problem Detail: I am undertaking a module in Concurrent Programming where some of the new content this year covers linearizability, the Java Memory Model, and sequential consistency. Our class slides are companion slides to The Art Of Multiprocessor Programming. I have Read More …
[Solved]: How can I check that the language of one context-free grammar is a subset of a second context-free grammar?
Problem Detail: Could you explain me, how can I check, that the language of first context-free grammar (G1) is a subset of the language of second context-free grammar (G2). G1 and G2 are two LL(1) grammars with identical alphabets: {a, b, Read More …
[Solved]: Can we break the Shannon capacity?
Problem Detail: I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver). The technique as Read More …
[Solved]: What is induction-induction?
Problem Detail: What is induction-induction? The resources I found are: the HoTT book, at the end of chapter 5.7. nLab’s article a paper called Inductive-inductive definitions this blog post also mentions inductive-inductive types The first two references are too brief for Read More …
[Solved]: Generating number of possibilites of popping two stacks to two other stacks
Problem Detail: Context: I’m working on this problem: There are two stacks here: A: 1,2,3,4 <- Stack Top B: 5,6,7,8 A and B will pop out to other two stacks: C and D. For example: pop(A),push(C),pop(B),push(D). If an item have been Read More …
[Solved]: Is the complexity class NP computably enumerable?
Problem Detail: The definition of the complexity class $mathsf{NP}$ seems to ensure (as good as possible) that it is computably enumerable. It looks as if the class could be enumerated by enumerating all Turing machines, and for each Turing machine report Read More …
[Solved]: Inferring refinement types
Problem Detail: At work I’ve been tasked with inferring some type information about a dynamic language. I rewrite sequences of statements into nested let expressions, like so: return x; Z => x var x; Z => let x = undefined in Read More …
