@techreport{TR-IC-14-03,
   number = {IC-14-03},
   author = {Rachid Rebiha and Arnaldo V. Moura and Nadir Matringe},
   title  =  {Automated  Generation  of  Asymptotically  Non-Terminant 
                   Initial Variable Values for Linear Programs},
   month = {January},
   year = {2014},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 37 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We present the new notion of \emph{asymptotically non-terminant
       initial  variable  values}  for  linear  loop  programs.  Those 
       specific  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-terminant initial variable values. Moreover,
       we  reduce  the  termination  problem of linear programs to the
       emptyness   check   of   a   specific   set  of  asymptotically 
       non-terminant   initial   variable   values.   Those  sets  are 
       represented  symbolically  and  exactly by a semi-linear space,
       \emph{e.g.}, conjunctions and disjunctions of linear equalities
       and inequalities. Also, by taking the complement of these sets,
       we  obtain  a  precise  under-approximations  of input sets for
       which linear programs do
  }
}