The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read–write memory. A task can be expressed as a relation between two chromatic simplicial complexes. The theorem states that a task has a protocol (algorithm) if and only if there is a certain color-preserving simplicial map compatible with that relation. The original proof of the ACT, given by Herlihy and Shavit (Proceedings of the 25th annual ACM symposium on theory of computing, pp 111–120, 1993; J ACM 46(6):858–923, 1999) relied on an involved geometric argument. Borowsky and Gafni (Proceedings of the 16th annual ACM symposium on principles of distributed computing, pp 189–198, 1997) later proposed an alternative proof based on a distributed algorithmic, termed the “convergence algorithm”. However the description of this algorithm was incomplete, and presented without proof. In this paper, we give the first complete description, along with a proof of correctness.
Journal of Applied and Computational Topology – Springer Journals
Published: May 29, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera