Update docs/src/starks/protocol_overview.md

Co-authored-by: Mauro Toscano <[email protected]>

docs/src/starks/protocol_overview.md

@@ -18,7 +18,7 @@ As mentioned in the Recap, the trace is a table containing the state of the syst
 
 The main tool in most proving systems is that of polynomials over a finite field  $\mathbb{F}$. Each column $T_j$ of the trace $T$ will be interpreted as evaluations of such a polynomial $t_j$. A consequence of this is that any type of information about the states must be encoded somehow as an element in $\mathbb{F}$.
 
-To ease notation we will assume here and in the protocol that the constraints encoding transition rules depend only on a state and the previous one. Everything can be easily generalized to transitions that depend on many preceeding states. Then, constraints can be expressed as multivariate polynomials in $2m$ variables
+To ease notation we will assume here and in the protocol that the constraints encoding transition rules depend only on a state and the previous one. Everything can be easily generalized to transitions that depend on many preceding states. Then, constraints can be expressed as multivariate polynomials in $2m$ variables
 $$P_k^T(X_1, \dots, X_m, Y_1, \dots, Y_m)$$
 A transition from state $i$ to state $i+1$ will be valid if and only if when we plug row $i$ of $T$ in the first $m$ variables and row $i+1$ in the second $m$ variables of $P_k^T$ we get $0$ for all $k$. In mathematical notation, this is
 $$P_k^T(T_{i, 0}, \dots, T_{i, m}, T_{i+1, 0}, \dots, T_{i+1, m}) = 0 \text{    for all }k$$