Editing Zeno's paradoxes (section)

==== Zeno behaviour ====
In the field of verification and design of [[timed event system|timed]] and [[hybrid system]]s, the system behaviour is called ''Zeno'' if it includes an infinite number of discrete steps in a finite amount of time.<ref name="Fishwick2007">{{cite book | editor=Paul A. Fishwick | title=Handbook of dynamic system modeling | chapter-url=https://books.google.com/books?id=cM-eFv1m3BoC&pg=SA15-PA22 | access-date=2010-03-05 | edition=hardcover | series=Chapman & Hall/CRC Computer and Information Science | date=1 June 2007 | publisher=CRC Press | location=Boca Raton, Florida, USA | isbn=978-1-58488-565-8 | pages=15–22 to 15–23 | chapter=15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling and Execution" by Pieter J. Mosterman, The Mathworks, Inc. | archive-date=2023-12-29 | archive-url=https://web.archive.org/web/20231229215249/https://books.google.com/books?id=cM-eFv1m3BoC&pg=SA15-PA22#v=onepage&q&f=false | url-status=live }}</ref> Some [[formal verification]] techniques exclude these behaviours from analysis, if they are not equivalent to non-Zeno behaviour.<ref>{{cite journal |last=Lamport |first=Leslie |author-link=Leslie Lamport |year=2002 |title=Specifying Systems |journal=Microsoft Research |publisher=Addison-Wesley |isbn=0-321-14306-X |url=http://research.microsoft.com/en-us/um/people/lamport/tla/book-02-08-08.pdf |page=128 |access-date=2010-03-06 |archive-date=2010-11-16 |archive-url=https://web.archive.org/web/20101116164613/http://research.microsoft.com/en-us/um/people/lamport/tla/book-02-08-08.pdf |url-status=live }}</ref><ref>{{cite journal  |last1=Zhang |first1=Jun |last2=Johansson| first2=Karl | first3=John  |last3=Lygeros |first4=Shankar |last4=Sastry   |title=Zeno hybrid systems | journal=International Journal for Robust and Nonlinear Control |year=2001 |access-date=2010-02-28  |doi=10.1002/rnc.592  |volume=11  |issue=5  |page=435 |s2cid=2057416 |url=http://aphrodite.s3.kth.se/~kallej/papers/zeno_ijnrc01.pdf |url-status=dead |archive-url=https://web.archive.org/web/20110811144122/http://aphrodite.s3.kth.se/~kallej/papers/zeno_ijnrc01.pdf |archive-date=August 11, 2011}}</ref> In [[systems design]] these behaviours will also often be excluded from system models, since they cannot be implemented with a digital controller.<ref>{{cite book|last2=Henzinger |first2=Thomas |last1=Franck |first1=Cassez |first3=Jean-Francois |last3=Raskin |url=http://mtc.epfl.ch/~tah/Publications/a_comparison_of_control_problems_for_timed_and_hybrid_systems.html |title=A Comparison of Control Problems for Timed and Hybrid Systems |year=2002 |access-date=2010-03-02 |url-status=dead |archive-url=https://web.archive.org/web/20080528193234/http://mtc.epfl.ch/~tah/Publications/a_comparison_of_control_problems_for_timed_and_hybrid_systems.html |archive-date=May 28, 2008 }}</ref>