Executable Transitive Closures


Title: Executable Transitive Closures
Author: René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at)
Submission date: 2012-02-29

We provide a generic work-list algorithm to compute the (reflexive-)transitive closure of relations where only successors of newly detected states are generated. In contrast to our previous work, the relations do not have to be finite, but each element must only have finitely many (indirect) successors. Moreover, a subsumption relation can be used instead of pure equality. An executable variant of the algorithm is available where the generic operations are instantiated with list operations.

This formalization was performed as part of the IsaFoR/CeTA project, and it has been used to certify size-change termination proofs where large transitive closures have to be computed.

  author  = {René Thiemann},
  title   = {Executable Transitive Closures},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2012,
  note    = {\url{http://isa-afp.org/entries/Transitive-Closure-II.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
License: GNU Lesser General Public License (LGPL)
Depends on: Regular-Sets