-
Burnside’s Lemma: Proof and Application
In the previous post, I proved the Orbit-Stabilizer Theorem which states that the number of elements in an orbit of a is equal to the number of left cosets of the stabilizer of a. Burnside’s Lemma Let’s us review the Lemma once again: Where A/G is the set of orbits, and |A/G| is the cardinality of this set. Ag is the […]
-
Burnside’s Lemma: Orbit-Stabilizer Theorem
Problem: Given a 3 by 3 grid, with 5 colors. How many different ways to color the grid, given that two configurations are considered the same if they can be reached through rotations ( 0, 90, 180, 270 degrees )? This problem was given in my Number Theory course. Somehow when I searched for the solution, […]
-
Bottom-up parsers
An in-depth discussion about bottom-up parsers’ concept, data structure and algorithm.
-
Top-down parsers
Context-free grammar: What and Why ? Introduction to top-down parsing.
-
Scanner: Categories
Types of scanners and their core’s algorithms.
-
Scanner: Automata and Regular Expression
from Regular Expression to Nondeterministic/ Deterministic Finite Automata.
-
Concurrency control
Serializability, Precedence Graph, Locking, Logging.
-
Naive Bayesian Spam Filter
Application of probability in implementing Naive Bayesian spam filter.
-
Linear Algebra – Things unsaid
Connecting the dots between various seemingly heterogenous concepts in linear algebra.