# This 90 Year Old Math Problem Shows Why We Need Quantum Computers

The notation thus permits us to seize the creating behavior of the machine and its tape through its consecutive IDs. Figure 2gives the first few consecutive IDs of \(T_\textrmSimple\) utilizing a graphical illustration. just isn’t Turing computable and so the identical is true of Thue’s problem. It can be very common to include the word computable when describing problems and solutions. We say that an issue is computable if an algorithm exists for solving it.

If A and B are equal, all a’s andb’s may have been erased and the machine strikes to state \(q_j\), else, it’s going to move to state \(q_n\). It is computed by \[\textrmCOMPARE\_\textrmERASE(\textrmCOMPARE\_\textrmALL(q_j,q_n,a,b),q_j,q_n,a,b)\] and so by recursively calling \(\textrmCOMPARE\_\textrmALL\). Note that each machine \(T_n\) has a singular D.N.; a D.N. There have to be a single block of symbols (a sequence of 1s representing some number or a logo representing one other sort of output) … Read More