321 

   321 

   322 

   322 

   323   For showing the undecidability of the halting problem, we need to consider

   323   For showing the undecidability of the halting problem, we need to consider

   324   two specific Turing machines.

   324   two specific Turing machines.

   325   

   325   

   326 *}

   328 *}

   327 

   329 

   328 section {* Abacus Machines *}

   330 section {* Abacus Machines *}

   329 

   331 

   330 section {* Recursive Functions *}

   332 section {* Recursive Functions *}