Problem Detail: After learning Haskell and other not so pure FP languages I decided to read about Category theory. After gaining good understanding of Category theory I started thinking about how the concepts of category theory can be used to think Read More …
Author: ignougroup
[Solved]: Why is the node with the greatest DFS post-order number not necessarily a sink?
Problem Detail: A sink in a directed graph is a node with no outgoing edges. If I perform a depth first search, why is it that the node with the least post-order number (and thus the highest pre-order number) not necessarily Read More …
[Solved]: Converting regular (Type-3) grammar to a deterministic finite state automaton
Problem Detail: I would like to create a deterministic finite state automaton (DFA) M=(Q, Σ, δ, q0, F) that is accepting the language generated by the following regular grammar (RG) G=(N, Σ, P, S). In short I want to convert RG Read More …
[Solved]: Rigorous proof against pseudo random function
Problem Detail: I have the following problem: Define the keyed function F as follows: On input k ∈ {0, 1}$^n$ and x ∈ {0, 1}$^n$ , Fk(x) = k ⊕ x.Rigorously prove that F is not a pseudorandom function. How do Read More …
[Solved]: Are there undecidable properties of non-turing-complete automata?
Problem Detail: Are there undecidable properties of linear bounded automata (avoiding the empty set language trick)? What about for a deterministic finite automaton? (put aside intractability). I would like to get an example (if possible) of an undecidable problem that is Read More …
[Solved]: Encoding the sequence 0110 and determining parity, data bit and value
Problem Detail: I’ve been struggling with several Hamming code/error detection questions because the logic behind it doesn’t seem to make sense. eg.1 eg.2 I don’t really understand the above two examples and the calculations taking place. How were the conclusions reached Read More …
[Solved]: Is it mandatory to define transitions on every possible alphabet in Deterministic Finite Automata?
Problem Detail: Tomorrow is my presentation and I want to clear my concepts… I’ve read that in DFA, “For each state, transition on all possible symbols (alphabet) should be defined.” Is for each state, defining transition on all possible symbols mandatory Read More …
[Solved]: What is the maximum number of shortest paths between any pair of vertices in a chordal graph?
Problem Detail: A graph $G$ is chordal if it doesn’t have induced cycles of length 4 or more. Chordal graphs are precisely the class of graphs that admit a clique tree representation. A clique tree $T$ of $G$ is a tree Read More …
[Solved]: How to XOR automata?
Problem Detail: Say we have 3 DFAs. We know how to OR, AND, or NOT them. But how does one XOR them? There is not one single mention of this online. $x; mathrm{XOR} ;y; mathrm{XOR} ;z = ((x|y)(neg x|y)|z) (neg ((x|y)(neg Read More …
[Solved]: Shor’s Algorithm speed
Problem Detail: I’m a fledgling computer science scholar, and I’m being asked to write a paper which involves integer factorization. As a result, I’m having to look into Shor’s algorithm on quantum computers. For the other algorithms, I was able to Read More …
