@MISC{SCMPDS_6.MIZ,
  AUTHOR = {Chen, Jing-Chao},
  TITLE = {The Construction and Computation of Conditional Statements for {SCMPDS}},
  NOTE = {This research is partially supported by the National Natural Science
       Foundation of China Grant No. 69873033.},
  SECTION1 = {Preliminaries},
  SECTION2 = {The Predicates of is\_closed\_on and is\_halting\_on},
  SECTION3 = {The Construction of Conditional Statements},
  SECTION4 = {The Computation of ``if var=0 then block1 else block2''},
  SECTION5 = {The Computation of ``if var=0 then block''},
  SECTION6 = {The Computation of ``if var<>0 then block''},
  SECTION7 = {The Computation of ``if var>0 then block1 else block2''},
  SECTION8 = {The Computation of ``if var>0 then block''},
  SECTION9 = {The Computation of ``if var<=0 then block''},
  SECTION10 = {The Computation of ``if var<0 then block1 else block2''},
  SECTION11 = {The Computation of ``if var<0 then block''},
  SECTION12 = {The Computation of ``if var>=0 then block''},
  DAY = {15},
  MONTH = {June},
  YEAR = {1999},
  ADDRESS1 = {Shanghai Jiaotong University},
  SUMMARY = {We construct conditional statements like
  the usual high level program language by program blocks of SCMPDS.
  Roughly speaking, the article justifies such a fact that
  when the condition of a conditional statement is true (false), and
  the true (false) branch is shiftable, parahalting and does not contain
  any halting instruction, and the false branch is shiftable, then it is
  halting and its computation result equals that of the true (false)
  branch. The parahalting means some program halts for all states, this
  is strong condition. For this reason, we introduce the notions of
  "is\_closed\_on" and "is\_halting\_on". The predicate "A is\_closed\_on B"
  denotes program A is closed on state B, and "A is\_halting\_on B" denotes
  program A is halting on state B. We obtain a similar theorem to
  the above fact by replacing parahalting by "is\_closed\_on" and
   "is\_halting\_on".}}

