Problem Detail: I was studying nondeterministic Turing Machines and came across the following question: Describe a nondeterministic Turing Machine (NTM) that only accepts two graphs (G1 and G2) if they are isomorphic, and provide the NSPACE. The NTM should use as Read More …
Author: ignougroup
[Solved]: Kolmogorov complexity of string concatenation
Problem Detail: If $K(s)$ is the Kolmogorov complexity of the string $s in {0,1}^*$, Can we prove (or disprove) the following statement: “Every string $s$ is a prefix of an incompressible string; i.e. for every string $s$ there exists a string Read More …
[Solved]: An interesting metric space related to Turing machines
Problem Detail: In this question we only consider Turing machines that halt on all inputs. If $k in mathbb{N}$ then by $T_k$ we denote the Turing machine whose code is $k$. Consider the following function $$s(x,y) = min{k mid |L(T_k) cap Read More …
[Solved]: Show that a language is RE or recursive
Problem Detail: Consider these 2 languages: $L_{ge5} = left { left< M right> : M text{ accepts at least 5 strings} right} $ $L_{<5} = left { left< M right> : M text{ accepts fewer than 5 strings} right}$ Are these Read More …
[Solved]: Help in understanding the implementation/application of scope trees
Problem Detail: I’m learning (self-taught) about language implementation and compiler design, and I’m implementing a toy language to cement the concepts in my mind. However, I’m having trouble understanding how scope trees are meant to be used. In my toy language, Read More …
[Solved]: It is possible to implement insertion sort for sorting linked list ?
Problem Detail: it is possible to implement insertion sort for sorting linked lists ? will it have the same O(n^2) efficiency as the array version ? Asked By : ghostloops Answered By : David Richerby This question is fully answered by the Wikipedia Read More …
[Solved]: Free and bound variables
Problem Detail: I am familiar with free and bound variables theory , but while learning I somewhere saw this lambda expression ((lambda var ((fn1 var) & (fn2 var))) argument) From what I have learned it seems to me as var is Read More …
[Solved]: What is a brief but complete explanation of a pure/dependent type system?
Problem Detail: If something is simple, then it should be completely explainable with a few words. This can be done for the λ-calculus: The λ-calculus is a syntactical grammar (basically, a structure) with a reduction rule (which means a search/replace procedure Read More …
[Solved]: Name of an Exact Cover by 3 sets variant
Problem Detail: Exact cover by 3-sets is $sf{NP}$-complete: Instance: Given a finite set $X = { x_1,x_2,…,x_{3n}}$ of $3n$ elements and a collection $C = { ( x_{i_1}, x_{i_2}, x_{i_3}) } $ of $m$ 3-elements subsets of $X$; Question: Find a Read More …
[Solved]: Range majority queries – most freqent element in range
Problem Detail: Given N numbers and M range queries (starting and ending points), I need to compute majority (most frequent element, if it exists) in these ranges. I’m looking for an algorithm that would answer queries in logarithmic or even constant Read More …
