2 research outputs found
On Termination of Polynomial Programs with Equality Conditions
We investigate the termination problem of a family of multi-path polynomial
programs (MPPs), in which all assignments to program variables are polynomials,
and test conditions of loops and conditional statements are polynomial
equalities. We show that the set of non-terminating inputs (NTI) of such a
program is algorithmically computable, thus leading to the decidability of its
termination. To the best of our knowledge, the considered family of MPPs is
hitherto the largest one for which termination is decidable. We present an
explicit recursive function which is essentially Ackermannian, to compute the
maximal length of ascending chains of polynomial ideals under a control
function, and thereby obtain a complete answer to the questions raised by
Seidenberg. This maximal length facilitates a precise complexity analysis of
our algorithms for computing the NTI and deciding termination of MPPs. We
extend our method to programs with polynomial guarded commands and show how an
incomplete procedure for MPPs with inequality guards can be obtained. An
application of our techniques to invariant generation of polynomial programs is
further presented
Robust Non-termination Analysis of Numerical Software
Numerical software are widely used in safety-critical systems such as
aircrafts, satellites, car engines and so on, facilitating dynamics control of
such systems in real time, it is therefore absolutely necessary to verify their
correctness. It is a long standing challenge to guarantee verified properties
of numerical software are indeed satisfied by their real behaviours, because
most of these verifications are conducted under ideal mathematical models, but
their real executions could be influenced essentially by uncertain inputs
accounting for round-off errors and additive perturbations from real-world
phenomena to hardware, which are abstracted away in these ideal mathematical
models. In this paper, we attempt to address this issue focusing on
nontermination analysis of numerical software, where nontermination is often an
unexpected behaviour of computer programs and may be problematic for
applications such as real-time systems having hard deadlines on transaction
execution time, and propose a method for robust conditional nontermination
analysis, which can be used to under-approximate the maximal robust
nontermination input set for a given program, from which the program never
terminates, regardless of the aforementioned disturbances. Finally, several
examples are employed to illustrate our approach.Comment: 10 pages, five figure