I will provide the code of the Vertex Coloring Algorithm and i need description of high level design with FSM diagrams and FSM table.And either give the pseudocode of actions or the pseudocode of the whole algorithm.The pictures are about Bully Algorithm. What i want is the same version of the FSM and FSM table of Vertex Coloring Algorithm that i will provide.

from mpi$4$py import MPI

import numpy as np

# MPI setup

comm $=$ MPI.COMM$\_$WORLD

rank $=$ comm.Get$\_$rank$()$

n $=$ comm.Get$\_$size$()$

# Message types

IDLE $=0$

COLORED $=1$

TERMINATE $=2$

ROUND $=0$

UPDATE $=1$

ACK $=2$

DISCARD $=3$

ROVER $=4$

TERMINATE $=5$

# Spanning tree of graph

ROOT $=0$

A $=$ np$.$array$([[0,0,0,1,1,0,0,1],$

$[0,0,0,0,0,1,0,1],$

$[0,0,0,1,1,0,1,0],$

$[1,0,1,0,1,0,1,0],$

$[1,0,1,1,0,1,0,1],$

$[0,1,0,0,1,0,0,1],$

$[0,0,1,1,0,0,0,0],$

$[1,1,0,0,1,1,0,0]],$ dtype$=$int$)$

children $=[[3],[],[4],[6],[7],[1],[2],[5]]$

parents $=[0,5,6,0,2,7,3,4]$

# Process state and communication variables

state $=$ IDLE

parent $=$ parents$[$rank$]$

childs $=$ set$($children$[$rank$])$

neighs $=$ indices$\_$set $=$ set$($i for i$,$ value in enumerate$($A$[$rank$])$ if value $==1)$

n$\_$neighs $=$ neighs.copy$()$

neighs$\_$received $=$ set$()$

rovers$\_$received $=$ set$()$

round$\_$received $=$ False

color $=-1$

banned$\_$colors $=$ set$()$

msg $=[-1,-1,$ None$]$ # sender$,$ type, data

round $=[-1,$ False$]$ # round number, round over

# Function to find the smallest available color

def find$\_$smallest$\_$available$\_$color$()$:

global banned$\_$colors

candidate$\_$color $=0$

while candidate$\_$color in banned$\_$colors:

candidate$\_$color $+=1$

return candidate$\_$color

# Function to check if the process has the highest degree in not colored neighbors

def highest$\_$degree$\_$in$\_$not$\_$colored$\_$neighbors$()$:

global n$\_$neighs

return not n$\_$neighs or rank $>$ max$($n$\_$neighs$)$

while state $!=$ TERMINATE:

round$[1]=$ False

neighs$\_$received.clear$()$

rovers$\_$received.clear$()$

round$\_$received $=$ False

if rank $==0$:

if state $==$ COLORED:

term$\_$msg $=$ msg$.$copy$()$

term$\_$msg$[0],$ term$\_$msg$[1]=$ rank, TERMINATE

comm.send$($obj$=$term$\_$msg$,$ dest$=$ROOT, tag$=$TERMINATE$)$

else:

round$[0]+=1$

round$\_$msg $=$ msg$.$copy$()$

round$\_$msg$[0],$ round$\_$msg$[1],$ round$\_$msg$[2]=$ rank, ROUND, round$[0]$

comm.send$($obj$=$round$\_$msg$,$ dest$=$ROOT, tag$=$ROUND$)$

while not round$[1]$:

sender$,\_$type, data $=$ comm.recv$()$

if $\_$type $==$ ROUND:

round$[0]=$ data

round$\_$msg $=$ msg$.$copy$()$

round$\_$msg$[0],$ round$\_$msg$[1],$ round$\_$msg$[2]=$ rank, ROUND, data

for child in childs:

comm.send$($obj$=$round$\_$msg$,$ dest$=$child, tag$=$ROUND$)$

if state $==$ COLORED:

discard$\_$msg $=$ msg$.$copy$()$

discard$\_$msg$[0],$ discard$\_$msg$[1]=$ rank, DISCARD

for neigh in neighs:

comm.send$($obj$=$discard$\_$msg$,$ dest$=$neigh, tag$=$DISCARD$)$

else:

if highest$\_$degree$\_$in$\_$not$\_$colored$\_$neighbors$()$:

color $=$ find$\_$smallest$\_$available$\_$color$()$

state $=$ COLORED

update$\_$msg $=$ msg$.$copy$()$

update$\_$msg$[0],$ update$\_$msg$[1],$ update$\_$msg$[2]=$ rank, UPDATE, color for neigh in n$\_$neighs:

comm.send$($obj$=$update$\_$msg$,$ dest$=$neigh, tag$=$UPDATE$)$

else:

discard$\_$msg $=$ msg$.$copy$()$

discard$\_$msg$[0],$ discard$\_$msg$[1]=$ rank, DISCARD

for neigh in neighs:

comm.send$($obj$=$discard$\_$msg$,$ dest$=$neigh, tag$=$DISCARD$)$

round$\_$received $=$ True

elif $\_$type $==$ UPDATE:

neighs$\_$received.add$($sender$)$

ack$\_$msg $=$ msg$.$copy$()$

ack$\_$msg$[0],$ ack$\_$msg$[1]=$ rank, ACK

comm.send$($obj$=$ack$\_$msg$,$ dest$=$sender$,$ tag$=$ACK$)$

if state $!=$ COLORED:

n$\_$neighs.remove$($sender$)$

banned$\_$colors.add$($data$)$

elif $\_$type $==$ DISCARD:

neighs$\_$received.add$($sender$)$

elif $\_$type $==$ ACK:

neighs$\_$received.add$($sender$)$

elif $\_$type $==$ ROVER:

rovers$\_$received.add$($sender$)$

elif $\_$type $==$ TERMINATE:

if childs:

for child in childs:

term$\_$msg $=$ msg$.$copy$()$

term$\_$msg$[0],$ term$\_$msg$[1]=$ rank, TERMINATE

state $=$ TERMINATE

break

# Check conditions for round completion

if round$\_$received and neighs.issubset$($neighs$\_$received$)$ and len$($childs$)==$ len$($rovers$\_$received$)$:

rover$\_$msg $=$ msg$.$copy$()$

rover$\_$msg$[0],$ rover$\_$msg$[1]=$ rank, ROVER

comm.send$($obj$=$rover$\_$msg$,$ dest$=$parent, tag$=$ROVER$)$

round$[1]=$ True

print$($f$\text{'}$I am rank $\{$rank$\}$ and my color $\{$color$\}\text{'})$