commit 72bb84a32fb03fc8fd68a5bbd3f10f9b34251440
parent ecd9359a645f2e42ba0bebc05d93755fa9f4ebdb
Author: AndrewLockVI <andrewlaack1@gmail.com>
Date: Mon, 3 Feb 2025 13:46:31 -0600
Took some more notes
Diffstat:
3 files changed, 17 insertions(+), 3 deletions(-)
diff --git a/definitions/Language.md b/definitions/Language.md
@@ -33,4 +33,3 @@ w_1 = 01010010
w_2 = abracadabra
\epsilon = empty string
-
diff --git a/definitions/NonDeterministicFiniteAutomata.md b/definitions/NonDeterministicFiniteAutomata.md
@@ -10,8 +10,12 @@
NOTE:
-Non-determinism is a generalization of determinism so every DFA is a NFA, but not necessarily the other direction, hence the statement above 'some edges may have'.
+Differences:
-Additionally, it is also possible for a NFA to have a state transition with a label of epsilon, indicating such a transition has no impact upon the current word.
+1. DFA must have transitions for each symbol whereas a NFA might not.
+2. It is possible for a NFA to have a state transition with a label of epsilon, indicating such a transition has no impact upon the current word.
+3. An NFA may have a state with multiple transitions for the same symbol.
When evaluating a NFA, if the machine runs into a split where it can either take one option or the other option, it creates a split (copy) and runs both in parallel. If the next input symbol does not appear on any of the arrows exiting the state occupied by the copy, the copy dies.
+
+A good way to think of NFAs is as a tree.
diff --git a/work/security/02-03-2025.md b/work/security/02-03-2025.md
@@ -0,0 +1,11 @@
+$\mathbb{Z}_m^*$ is the unit group of $\mathbb{Z_m}$ that with an inverse in $\mathbb{Z}_m$. This is all elements s.t. gcd(a,m) = 1.
+
+Z_4 = {0,1,2,3}
+
+gcd(1,4) = 1, gcd(3,4) = 1, gcd(2,4) = 2
+
+So Z_4^* = {1,3}.
+
+This is the set of the Euler Totient Function, and it's cardinality is the Eurler Totient Function's output of the specified number.
+
+Totient function is also sometimes referred to as Euler's phi function.
