Proving program correctness
I want to prove the correctness of iterative method for square root of "a" as given below:
s,m := 0, a
while m > ε/2
if (s+m)^2 <= a
s := s + m
m := m /2
I have been given a precondition $$Q: a = a' ∧ a > 1$$ and postcondition $$R: Q ∧ |s^{2} - a| < varepsilon$$
and a loop invariant $$P: Q ∧ |s^{2} - a| < 2m$$
Can you please prove or disprove $$P∧Mgeqfrac{varepsilon}{2} wedge |(S+M)^{2}- A|leq A Rightarrow |(S+M)^{2}- A| < 2M$$
Thanks in advance!
algorithms computer-science
asked Nov 19 '18 at 2:40
King Lear
1
add a comment |
I want to prove the correctness of iterative method for square root of "a" as given below:
s,m := 0, a
while m > ε/2
if (s+m)^2 <= a
s := s + m
m := m /2
I have been given a precondition $$Q: a = a' ∧ a > 1$$ and postcondition $$R: Q ∧ |s^{2} - a| < varepsilon$$
and a loop invariant $$P: Q ∧ |s^{2} - a| < 2m$$
Can you please prove or disprove $$P∧Mgeqfrac{varepsilon}{2} wedge |(S+M)^{2}- A|leq A Rightarrow |(S+M)^{2}- A| < 2M$$
Thanks in advance!
algorithms computer-science
asked Nov 19 '18 at 2:40
King Lear
1
Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36
add a comment |
I want to prove the correctness of iterative method for square root of "a" as given below:
s,m := 0, a
while m > ε/2
if (s+m)^2 <= a
s := s + m
m := m /2
I have been given a precondition $$Q: a = a' ∧ a > 1$$ and postcondition $$R: Q ∧ |s^{2} - a| < varepsilon$$
and a loop invariant $$P: Q ∧ |s^{2} - a| < 2m$$
Can you please prove or disprove $$P∧Mgeqfrac{varepsilon}{2} wedge |(S+M)^{2}- A|leq A Rightarrow |(S+M)^{2}- A| < 2M$$
Thanks in advance!
algorithms computer-science
asked Nov 19 '18 at 2:40
King Lear
1
I want to prove the correctness of iterative method for square root of "a" as given below:
s,m := 0, a
while m > ε/2
if (s+m)^2 <= a
s := s + m
m := m /2
I have been given a precondition $$Q: a = a' ∧ a > 1$$ and postcondition $$R: Q ∧ |s^{2} - a| < varepsilon$$
and a loop invariant $$P: Q ∧ |s^{2} - a| < 2m$$
Can you please prove or disprove $$P∧Mgeqfrac{varepsilon}{2} wedge |(S+M)^{2}- A|leq A Rightarrow |(S+M)^{2}- A| < 2M$$
Thanks in advance!
algorithms computer-science
algorithms computer-science
asked Nov 19 '18 at 2:40
King Lear
1
asked Nov 19 '18 at 2:40
King Lear
1
asked Nov 19 '18 at 2:40
King Lear
1
asked Nov 19 '18 at 2:40
King Lear
1
asked Nov 19 '18 at 2:40
King Lear
1
1
Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36
add a comment |
Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36
Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36
Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36
add a comment |
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Hi, in your code as written, if $s$ and $m$ start as 0, $m$ will always be 0 and $s$ will never change, so program is clearly incorrect. I also don't understand what is $a^{prime}$.
– Todor Markov
Nov 19 '18 at 9:36