A recursive decision method for termination of linear programs

In their CAV 2004 and 2006 papers, Tiwari and Braverman have proved that, for a class of linear programs over the reals, termination is decidable. In this paper, we propose a new algorithm to decide whether a program of the same class terminates or not. In our approach, a program with an assignment matrix having a single Jordan block or having several Jordan blocks with the same eigenvalue is treated as a basic program to which we reduce a program with arbitrary assignment matrices in a recursive process. Furthermore, if a basic program is non-terminating, our method constructs at least one point on which a given basic program does not terminate. In contrast, for a non-terminating basic program, in most cases, the methods of Tiwari and Braverman provide only a so-called N-nonterminating point. Also, different from their methods, we do not need to guess a dominant term from every loop condition in our recursive procedure.