Update text

docs/src/booklet/4-encoding.md

@@ -1,8 +1,8 @@
 # Encoding Methods
 
-## Variable Encoding
+## Variables
 
-As you should already know, QUBO models are comprised only of binary variables.
+As you may already know, QUBO models are comprised only of binary variables.
 So when we are reformulating general optimization problems, one important step is to encode variables into binary ones. 
 
 `ToQUBO` currently implements 6 encoding techniques.
@@ -11,30 +11,28 @@ Also, they differ in the magnitude of their coefficients ``\Delta``.
 
 | Encoding              | Binary Variables   | # Linear terms   | # Quadratic terms   | ``\Delta``       |
 |:---------------------:|:------------------:|:----------------:|:-------------------:|:----------------:|
-| Binary                |  ``O(log \ n)``    |  ``O(log \ n)``  |      -              | ``O(n)``         |
+| Binary                |  ``O(\log n)``     |  ``O(\log n)``   |      -              | ``O(n)``         |
 | Unary                 |    ``O(n)``        |    ``O(n)``      |      -              | ``O(1)``         |
 | One-Hot               |    ``O(n)``        |    ``O(n)``      |      ``O(n^2)``     | ``O(n)``         |
 | Domain-Wall           |    ``O(n)``        |    ``O(n)``      |      ``O(n)``       | ``O(n)``         |
 | Bounded-Coefficient   |    ``O(n)``        |    ``O(n)``      |       -             | ``O(1)``         |
 | Arithmetic Prog       |  ``O(\sqrt{n})``   |  ``O(\sqrt{n})`` |       -             | ``O(\sqrt{n})``  |
 
 
-### Linear Encoding Methods
+### Linear Encoding
 ```@docs
-ToQUBO.Mirror
-```
-
-```@docs
-ToQUBO.LinearEncoding
 ToQUBO.Binary
 ToQUBO.Unary
 ToQUBO.Arithmetic
 ToQUBO.OneHot
 ```
 
-### Sequential Encoding Methods
 ```@docs
-ToQUBO.SequentialEncoding
+ToQUBO.Mirror
+```
+
+### Sequential Encoding
+```@docs
 ToQUBO.DomainWall
 ```
 
@@ -43,13 +41,14 @@ ToQUBO.DomainWall
 ToQUBO.Bounded
 ```
 
-## Constraint Encoding
+## Constraints
 
-A QUBO model is unconstrained. So when `ToQUBO` is reformulating a problem, it needs to encode all constraints into the objective function loosing as little information as possible.
+A QUBO model is unconstrained. So when `ToQUBO` is reformulating a problem, it needs to encode all constraints into the objective function losing as little information as possible.
 
-As constraints are introduced into the objective function, we need to make sure that they won't be violated. In order to do that, `ToQUBO` multiplies the encoded constraint by a large penalty $\rho$, so that any violation would result in an infeasible solution to the problem.
+As constraints are introduced into the objective function, we need to make sure that they won't be violated.
+In order to do that, `ToQUBO` multiplies the encoded constraint by a large penalty ``\rho``, so that any violation would result in a sub-optimal solution to the problem.
 
-Sometimes, moving a constraint to the objective fuction might introduce higher-order terms (degree > 2). If that is the case, `ToQUBO` needs to reduce it back to a quadratic function. 
+Sometimes, the encoding process might introduce higher-order terms, demanding `ToQUBO` to reduce the offending polynomials back to a quadratic form. 
 
 As of today, `ToQUBO` provides encoding for the following constraints: