@techreport{TR-IC-13-07,
   number = {IC-13-07},
   author = {Rachid Rebiha and Nadir Matringe and Arnaldo V. Moura},
   title  =  {Necessary  and  Sufficient  Condition for Termination of
                   Linear Programs},
   month = {February},
   year = {2013},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 22 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       We describe new decidability results that respond completely to
       major  conjectures  on  termination  analysis  of  linear  loop 
       programs,  on all initial values interpreted over the reals. To
       the  best  of our knowledge, we present the first necessary and
       sufficient   conditions   from  which  we  provide  a  complete 
       decidability  result  and  methods  for termination analysis of
       such  a  class of programs. We reduce the termination analsysis
       for  such  programs  to the problem consisting in checking if a
       specific vector (related to the loop condition encoding) belong
       to  a  specific  vectorial space related to the matrix encoding
       the  assignements of the loop variables. We provide theoretical
       results  guaranteeing  the  soundness  and  completeness of the
       termination   analysis   while   restrincting   the   variables  
       interpretation  over  a specific countable subring of the field
       of real numbers.
  }
}