Problem Detail: Edit: My original question referred to nonconstructive and constructive definitions of function types. I changed the terminology in the question and the title to semantic and syntactic, which the answer indicates is the correct terminology for this distinction. I Read More …
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[Solved]: Dynamic programming VS Greedy Algroithms
Problem Detail: I have two True or False questions in my practice test that are related but I am unsure about: 1. If an optimization problem can be solved using a greedy algorithm, there must be a solution for this optimization Read More …
[Solved]: Can I construct a Turing machine that accepts only its own encoding?
Problem Detail: Is the set $S$ = $lbrace M mid M text{ is a Turing machine and }L(M)=lbrace langle Mranglerbracerbrace$ empty? In other words is there a Turing machine $M$ that only accepts its own encoding? What about a Turing machine Read More …
[Solved]: Maximum Independent Subset of 2D Grid Subgraph
Problem Detail: In the general case finding a Maximum Independent Subset of a Graph is NP-Hard. However consider the following subset of graphs: Create an $N times N$ grid of unit square cells. Build a graph $G$ by creating a vertex Read More …
[Solved]: How to find the maximal set of elements $S$ of an array such that every element in $S$ is greater than or equal to the cardinality of $S$?
Problem Detail: I have an algorithmic problem. Given an array (or a set) $T$ of $n$ nonnegative integers. Find the maximal set $S$ of $T$ such that for all $ain S$, $ageqslant |S|$. For example: If $T$=[1, 3, 4, 1, 3, Read More …
[Solved]: Time complexity based on two variables
Problem Detail: Suppose we have a function based on two inputs of length $m,n$. Therefore the time complexity of the function is calculated by $T(m,n)$. Suppose that we have: $T(m,c)in O(m^2)$ for any constant $c$. $T(c’,n)in O(n^2)$ for any constant $c’$. Read More …
[Solved]: How to go from a recurrence relation to a final complexity
Problem Detail: I have an algorithm, shown below, that I need to analyze. Because it’s recursive in nature I set up a recurrence relation. //Input: Adjacency matrix A[1..n, 1..n]) of an undirected graph G //Output: 1 (true) if G is complete Read More …
[Solved]: Categorisation of type systems (strong/weak, dynamic/static)
Problem Detail: In short: how are type systems categorised in academic contexts; particularly, where can I find reputable sources that make the distinctions between different sorts of type system clear? In a sense the difficulty with this question is not that Read More …
[Solved]: How to convert an NFA with overlapping cycles into a regular expression?
Problem Detail: If I understand correctly, NFA have the same expressive power as regular expressions. Often, reading off equivalent regular expressions from NFA is easy: you translate cycles to stars, junctions as alternatives and so on. But what to do in Read More …
[Solved]: Maximum degree of concurrency in task dependency graphs
Problem Detail: I’ve been researching ways of modeling and executing tasks which are dependent on each other (but in an acyclic way) and came up with task graphs. But the question that’s bugging me is how can I find out the Read More …
