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LSV Seminars
http://www.lsv.ens-cachan.fr
Seminars of the Laboratoire Spécification et Vérification at ENS Cachanhttp://www.lsv.ens-cachan.fr/Seminaires/2017-03-29T21:26:14+02:00daily6Joost-Pieter Katoen: Runtime Analysis of Randomized Algorithms: A Dijkstra Déjà Vu
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201703291000
Randomization is an important tool in algorithm design for obtaining
efficient solutions; e.g., random pivot selection in quicksort lowers
the expected runtime (ER) to O(n log n). Reasoning about the ER of
randomized algorithms is subtle and full of nuances, as:
they may have diverging runs but have a finite ER;
they may almost surely terminate but have an infinite ER;
running two finite-ER algorithms in sequence may yield an infinite ER.
ER analysis of randomized algorithms is typically done using classical
probability theory, mostly with arguments relying on random variable
expectations or martingales. These analyses partially follow an ad-hoc
reasoning and take non-trivial relationships between random variables
for granted.
In this talk, I'll present a formal verification approach towards the ER
analysis using a weakest-precondition approach Ã la Dijkstra. It allows
e.g. to prove the positive almost-sure termination: does a program
terminate with probability one in finite expected time? We show proof
rules for loops prove the soundness w.r.t a simple operational mode and
argue that our approach conservatively extends Nielson's approach for
deterministic programs. Sébastien Bardin and Richard Bonichon: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201705021100
Colin Riba: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201706131100
Pablo Arrighi: TBA
http://www.lsv.ens-cachan.fr/Seminaires/#semLSV.201706201100