Problem Detail: A binary sequence of length $n$ is just an ordered sequence $x_1,ldots,x_n$ so that each $x_j$ is either $0$ or $1$. In order to generate all such binary sequences, one can use the obvious binary tree structure in the Read More …
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[Solved]: HamCycle to HamPath reduction
Problem Detail: I’ve seen a reduction that’s done by adding another vertex to the graph and creating a path through that vertex. Why do I need to add a vertex? Cant I just remove an edge? Lets say the graph with Read More …
[Solved]: Can any finite problem be in NP-Complete?
Problem Detail: My lecturer made the statement Any finite problem cannot be NP-Complete He was talking about Sudoku’s at the time saying something along the lines that for a 8×8 Sudoku there is a finite set of solutions but I can’t Read More …
[Solved]: Tree data structure for fast merges
Problem Detail: I need trees that have the following properties: Each node in the tree has two values associated with it – a key and an associated opaque data element. An internal node in the tree has unbounded number of children. Read More …
[Solved]: Does immutability in functional programming really exist?
Problem Detail: Although I work as a programmer in my daily life and use all the trendy languages (Python, Java, C, etc) I still have no clear view of what functional programming is. From what I’ve read, one property of functionally Read More …
[Solved]: Closure against right quotient with a fixed language
Problem Detail: I’d really love your help with the following: For any fixed $L_2$ I need to decide whether there is closure under the following operators: $A_r(L)={x mid exists y in L_2 : xy in L}$ $A_l(L)={x mid exists y in Read More …
[Solved]: Why are computable functions also called recursive functions?
Problem Detail: In computability theory, computable functions are also called recursive functions. At least at first sight, they do not have anything in common with what you call “recursive” in day-to-day programming (i.e., functions that call themselfes). What is the actual Read More …
[Solved]: Draw a DFA that accepts ((aa*)*b)*
Problem Detail: A homework question asks me to a draw a DFA for the regular expression $((aa^*)^*b)^*$ I’m having trouble with this because I’m not sure how to express the idea of $a$ followed by $0$ or many $a$’s many times, Read More …
[Solved]: Are “Flow Free” puzzles NP-hard?
Problem Detail: A “Flow Free” puzzle consists of a positive integer $n$ and a set of (unordered) pairs of distinct vertices in the $n times n$ grid graph such that each vertex is in at most one pair. A solution to Read More …
[Solved]: Decidable restrictions of the Post Correspondence Problem
Problem Detail: The Post Correspondence Problem (PCP) is undecidable. The bounded version of the PCP is $mathrm{NP}$-complete and the marked version of the PCP (the words of one of the two lists are required to differ in the first letter) is Read More …
