On Termination of Integer Linear Loops

  title={On Termination of Integer Linear Loops},
  author={Jo{\"e}l Ouaknine and Jo{\~a}o Sousa Pinto and James Worrell},
A fundamental problem in program verification concerns the termination of simple linear loops of the form: x← u ; while Bx ≥ b do x← Ax+ a , where A and B are integer matrices, and u, a, and b are integer vectors. We give a decision procedure for the problem of whether such a loop terminates for all initial integer vectors u, provided that the matrix A is diagonalisable. The correctness of our algorithm relies on sophisticated tools from algebraic and analytic number theory, Diophantine… CONTINUE READING
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