It is logically impossible to draw a square circle because it
must be perfectly round AND not round at all with four equal
length sides.
It is clear that the impossibility of creating a CAD system that
can correctly draw square circles places no limits on what
computers can do.
It is less clear that requiring a program H to report on the behavior
of another program D that does the opposite of whatever H says
is a logical impossibility when we see that program H1 can correctly
say what D will do.
When we get back to the original {halting problem} we can see
that no program H can ever always say what every program
D will do because some D will do the opposite of whatever H says.
So the when the {halting problem} requires a program H to always
say whatever program D will do includes programs that do the
opposite of whatever H says this is requiring the logically impossible,
thus the same as requiring a CAD system to correctly draw square circles.
The {halting problem} as defined requires the logically impossible
therefore it places no actual limits on what can be computed.
This above is based on my own work since 2004 that did not become
clear enough to understand until I discussed this with Professor Hehner
based on his equivalent ideas.
Objective and Subjective Specifications
Professor Rick Hehner PhD (2017)
must be perfectly round AND not round at all with four equal
length sides.
It is clear that the impossibility of creating a CAD system that
can correctly draw square circles places no limits on what
computers can do.
It is less clear that requiring a program H to report on the behavior
of another program D that does the opposite of whatever H says
is a logical impossibility when we see that program H1 can correctly
say what D will do.
When we get back to the original {halting problem} we can see
that no program H can ever always say what every program
D will do because some D will do the opposite of whatever H says.
So the when the {halting problem} requires a program H to always
say whatever program D will do includes programs that do the
opposite of whatever H says this is requiring the logically impossible,
thus the same as requiring a CAD system to correctly draw square circles.
The {halting problem} as defined requires the logically impossible
therefore it places no actual limits on what can be computed.
This above is based on my own work since 2004 that did not become
clear enough to understand until I discussed this with Professor Hehner
based on his equivalent ideas.
Objective and Subjective Specifications
Professor Rick Hehner PhD (2017)
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