The Equivalence Problem of Simple Programs

Many problems, some of them quite meaningful, have been proved to be recursively unsolvable for programs in general. The paper is directed toward a class of programs where many decision problems are solvable. The equivalence problem has been proved to be unsolvable for the class <italic>L</italic><subscrpt>2</subscrpt> of loop programs defining the class of elementary functions. A solution is given for the class <italic>L</italic><subscrpt>1</subscrpt> defining the class of simple functions. Further, a set of other decision problems not directly connected with the equivalence problem is investigated. These problems are found again to be unsolvable for the class <italic>L</italic><subscrpt>2</subscrpt>; but as before, a solution is given for the class <italic>L</italic><subscrpt>1</subscrpt>. It is concluded, therefore, that there is a barrier of unsolvability between the classes <italic>L</italic><subscrpt>1</subscrpt> and <italic>L</italic><subscrpt>2</subscrpt>.