@techreport{TR-IC-14-08,
   number = {IC-14-08},
   author = {Rachid Rebiha and Arnaldo V. Moura and Nadir Matringe},
   title  =  {Characterization  of  Termination for Linear Homogeneous
                   Programs},
   month = {June},
   year = {2014},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 25 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We   present   necessary  and  sufficient  conditions  for  the 
       termination  of  linear homogeneous programs. We also develop a
       powerful computational method to determine termination for this
       class of programs. Our complete characterization of termination
       for  such  programs  is  based  on linear algebraic methods. We
       reduce  the verification of the termination problem to checking
       the  orthogonality  of  a  well  determined  vector space and a
       certain vector, both related to loops in the program. Moreover,
       we  provide  theoretical  results  and  symbolic  computational 
       methods  guaranteeing the soundness, completeness and numerical
       stability  of  the approach. Finally, we show that it is enough
       to  interpret  variable values over a specific countable number
       field,  or  even  over  its ring of integers, when one wants to
       check termination over the reals.
  }
}