#OK to post homework
#Salman Manzoor 03-02-2025, Assignment 10

read `C10.txt`:

SimulateNAND:=proc(n,k,K) local i,sum:
sum:=0:
for i from 1 to K do
	sum:=sum+nops(EvalSP(RSLP(n,k),n)):
od:
sum/K:
end:

Monotone:=proc(n,k,p) local P,i,i1,j1,gate:
P:=[seq(i,i=1..n)]:
for i from n+1 to k+n do
	i1:=rand(1..nops(P))():
	j1:=rand(1..nops(P))():
	gate:=1:
	if (evalb(rand(1..denom(p))()<=numer(p))) then gate:=2 fi: 
	P:=[op(P),[i1,j1,gate]]:
od:
P:
end:

EvalMP1:=proc(P,IN) local n,P1,i,i1,j1,k:
P1:=IN:
n:=nops(IN):
for i from n+1 to nops(P) do
	i1:=P[i][1]:
	j1:=P[i][2]:
	k:=AND(P1[i1],P1[j1]):
	if (P[i][3]=1) then k:=OR(P1[i1],P1[j1]): fi:
	P1:=[op(P1),k]:
od:
P1[-1]:
end:

EvalMP:=proc(P,n) local V,v,T:
V:=TF(n):
T:={}:
for v in V do
 if EvalMP1(P,v) then
   T:=T union {v}:
 fi:
od:
T:
end:

SimulateMonotone:=proc(n,k,p,K) local i,sum:
sum:=0:
for i from 1 to K do
	sum:=sum+nops(EvalMP(Monotone(n,k,p),n)):
od:
sum/K:
end:

#The SimulateNAND tests gave [693.7600000, 664.6560000, 643.3480000, 636.93300000]
#The SimulateMonotone tests gave [505.0880000, 507.4640000, 517.7280000,
# 499.7220000, 379.9360000, 341.6560000, 306.6000000, 238.1860000,
# 216.5920000, 172.9920000, 109.3000000, 53.22500000]