COGS 2160 Lecture Notes - Lecture 4: Universal Turing Machine, Halting Problem, Alonzo Church

• School: York University
• Department: Cognitive Science
• Course: COGS 2160
• Professor: Muhammad Ali Khalidi

Document Summary

Computation is what computers do and, according to many cognitive scientists, it is what minds do. What turing gave us was a theoretical model that many have thought to capture the essence of computation. Turi(cid:374)g"s (cid:373)odel (the so-called turing machine) is one of the most important and i(cid:374) ue(cid:374)tial ideas i(cid:374) (cid:272)og(cid:374)iti(cid:448)e s(cid:272)ie(cid:374)(cid:272)e, e(cid:448)e(cid:374) though it i(cid:374)itially see(cid:373)s to ha(cid:448)e little to do with the human mind. Algorithm: a finite rule or procedure for solving a problem: this can involve carrying out a calculation, computing a fu(cid:374)(cid:272)tio(cid:374), e(cid:448)e(cid:374) fi(cid:374)di(cid:374)g a friend. Ma(cid:374)y (cid:272)o(cid:373)puter progra(cid:373)s are (cid:374)ot de (cid:374)ed for e(cid:448)ery possi(cid:271)le i(cid:374)put. They will give a solution for some inputs, the ones for which they are de (cid:374)ed. But for other i(cid:374)puts, the o(cid:374)es for (cid:449)hi(cid:272)h they are (cid:374)ot de (cid:374)ed, they (cid:449)ill just e(cid:374)dlessly loop, looki(cid:374)g for a solutio(cid:374) that is(cid:374)"t there.