A Framework for Verified Depth-First Algorithms

René Neumann

doi:10.29007/8hkx

Download PDF Open PDF in browser

A Framework for Verified Depth-First Algorithms

10 pages•Published: July 28, 2013

René Neumann

Abstract

We present a framework in Isabelle/HOL for formalizing variants of
depth-first search. This framework allows to easily prove non-trivial
properties of these variants. Moreover, verified code in several
programming languages including Haskell, Scala and Standard ML can be
generated.

In this paper, we present an abstract formalization of depth-first search and
demonstrate how it is refined to an efficiently executable version. Further we use the emptiness-problem of Büchi-automata known from model checking as the motivation to present three Nested DFS algorithms. They are formalized, verified and transformed into executable code using our framework.

Keyphrases: depth-first search, Isabelle/HOL, model checking, theorem proving

In: Jacques Fleuriot, Peter Höfner, Annabelle McIver and Alan Smaill (editors). ATx'12/WInG'12: Joint Proceedings of the Workshops on Automated Theory eXploration and on Invariant Generation, vol 17, pages 36--45

Links:	https://easychair.org/publications/paper/TLd9
	https://doi.org/10.29007/8hkx

BibTeX entry

@inproceedings{ATx'12/WInG'12:Framework_for_Verified_Depth_First,
  author    = {Ren\textbackslash{}'e Neumann},
  title     = {A Framework for Verified Depth-First Algorithms},
  booktitle = {ATx'12/WInG'12: Joint Proceedings of the Workshops on Automated Theory eXploration and on Invariant Generation},
  editor    = {Jacques Fleuriot and Peter H\textbackslash{}"ofner and Annabelle McIver and Alan Smaill},
  series    = {EPiC Series in Computing},
  volume    = {17},
  pages     = {36--45},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/TLd9},
  doi       = {10.29007/8hkx}}

Download PDF Open PDF in browser