Hypercomputation: computing more than the Turing machine

Hypercomputation or super-Turing computation refers to models of computation that can provide outputs that are not Turing computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that can correctly evaluate every statement in Peano arithmetic.

Basically, a system able to perform countable infinite computational steps within a finite time.

In laymans terms, Hypercomputing and Hypercomputers are way beyond any classical computer we have today or any quantum computer. It borders on ‘infinite’ ‘god’ like powers of computation. Which is why everyone is interested in it.

Various theoretical models for such hypercomputation aka Hypermachines or Hypercomputers

O-machines

TM’s with initial inscription

Coupled TM’s

Asynchronous networks of TM’s

Error prone TM’s

Probabilistic TM’s

Infinite state TM’s

Accelerated TM’s

Infinite time TM’s

Fair non-deterministic TM’s

O-machines or Oracle machines are some fantasy machines with an absolutely magical oracle which knows all the answers, but nobody can explain how it does so. So from Automatski’s standpoint O-machines are a No Go!

And since we will never be able to physically build a machine with ‘Infinite’ state or time. Or basically infinite of anything. These machines are great for theoretical analysis and mind experiments. But again a No Go!

Similarly Probabilistic TM’s lead to Exponential Complexity Computations. And are a No Go!

Accelerated TM’s are basically built on some super fast physical process. But however fast it is. It will never be able to solve Exponential Complexity problems. Hence this too is a No Go!

Conclusion

So that leaves us with (things we are pursueing at Automatski)

Coupled TM’s

Asynchronous networks of TM’s

Error prone TM’s

Fair non-deterministic TM’s

These are all promising concepts. Along with our other efforts on Quantum Gravity Computers.

Someone will ask if we have a QGC why do we bother with these 4? The answer is it is always benefitial and also it is what we do at Automatski. To pursue multiple approaches together. It gives us multiple perspectives, reduces our risks and drives breakthrough inventions and innovation.