@techreport{TR-IC-14-09,
   number = {IC-14-09},
   author = {Rachid Rebiha and Arnaldo V. Moura and Nadir Matringe},
   title  =  {Generating Asymptotically Non-Terminating Initial Values
                   for Linear Programs},
   month = {June},
   year = {2014},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 35 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We  present  the notion of \emph{asymptotically non-terminating
       initial variable values} for linear loop programs. Those values
       are  directly  associated  to initial variable values for which
       the  corresponding  program does not terminate. Our theoretical
       contributions  provide  us  with powerful computational methods
       for    automatically    generating   sets   of   asymptotically  
       non-terminating   initial   variable   values.  Such  sets  are 
       represented  symbolically  and  exactly by a semi-linear space,
       \emph{e.g.},  characterized by conjunctions and disjunctions of
       linear  equalities  and inequalities. Moreover, by taking their
       complements, we obtain a precise under-approximation of the set
       of  inputs  for which the program does terminate, thus reducing
       the  termination  problem  of  linear programs to the emptiness
       check of a specific set of asymptotically non-terminant initial
       variable  values.  Our \emph{static input data analysis} is not
       restricted only to programs where the variables are interpreted
       over  the  reals.  We  extend  our  approach  and  provide  new 
       decidability  results  for  the  termination  problem of affine
       integer and rational programs.
  }
}