ABSTRACT
The initial aim of recursion theory was to show that certain problems of the form "Find an algorithm by which " were unsolvable. This chapter gives a few examples of such problems. It discusses the halting problem, statusword, and word problems for certain semigroups. Symmetric processes are interesting because of their relation to semigroups. Using Church's Thesis, the chapter looks at its first unsolvable problem. It follows that the halting program is unsolvable.
