In a unit-cost random access machine, the IF-THEN-construct can be simulated using basic $$L O O P$$ commands as well as the algorithm for $$r_i:=c$$ and the algorithm for the NOP operation.

# Algorithm: Conditional execution of $$L O O P$$ programs - IF-THEN-ELSE construct

class UCRAM(): # unit-cost random access machine with 3 registers r_i = 0 r_m = 0 r_n = 0

  def set_r_m_to_1(self):
# set r_m=0 with loop r_m do
while True:
if self.r_m &gt; 0:
self.r_m = self.r_m - 1 #  LOOP register n
self.NOP() #  DO nothing
else:
break
# set register m to 1 by incrementing it once
self.r_m = self.r_m + 1

def set_r_n_to_1(self):
# set r_n=0 with loop r_n do
while True:
if self.r_n &gt; 0:
self.r_n = self.r_n - 1 #  LOOP register n
self.NOP() #  DO nothing
else:
break
# set register n to 1 by incrementing it once
self.r_n = self.r_n + 1

def LOOP_r_i_DO_decrement_r_n(self):
while True:
if self.r_i &gt; 0:
self.r_i = self.r_i - 1 #  LOOP register i
if self.r_n &gt; 0:
self.r_n = self.r_n - 1  # DO decrement register n
else:
break

def LOOP_r_n_DO_decrement_r_m(self):
while True:
if self.r_n &gt; 0:
self.r_n = self.r_n - 1 #  LOOP register n
if self.r_m &gt; 0:
self.r_m = self.r_m - 1  # DO decrement register m
else:
break

def LOOP_r_n_DO_P1(self):
while True:
if self.r_n &gt; 0:
self.r_n = self.r_n - 1 #  LOOP register n
# DO P1 and DO decrement register m
self.P1()
if self.r_m &gt; 0:
self.r_m = self.r_m - 1
else:
break

def LOOP_r_m_DO_P2(self):
while True:
if self.r_m &gt; 0:
self.r_m = self.r_m - 1  # LOOP register m
self.P2()
else:
break

def P1(self):
print("executing P1")

def P2(self):
print("executing P2")

def IF_ri_THEN_P1_ELSE_P2_END(self):
self.set_r_m_to_1()
self.set_r_n_to_1()
self.LOOP_r_i_DO_decrement_r_n()
self.LOOP_r_n_DO_P1()
self.LOOP_r_n_DO_decrement_r_m()
self.LOOP_r_m_DO_P2()

1. Usage of simulating an IF r_i==0 THEN P1 ELSE P2 END construct
2. creating a unit-cost access machine ucram = UCRAM() ucram.r_i = 100 ucram.IF_ri_THEN_P1_ELSE_P2_END() ucram.r_i = 0 ucram.IF_ri_THEN_P1_ELSE_P2_END()

3. will output

4. executing P2
5. executing P2

Algorithms: 1 2
Examples: 3

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### References

#### Bibliography

1. Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition