{"id":338555,"date":"2016-12-19T13:22:45","date_gmt":"2016-12-19T21:22:45","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=338555"},"modified":"2018-10-16T21:01:59","modified_gmt":"2018-10-17T04:01:59","slug":"mutual-exclusion-problem-part-ii-statements-solutions","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/mutual-exclusion-problem-part-ii-statements-solutions\/","title":{"rendered":"The Mutual Exclusion Problem – Part II: Statements and Solutions"},"content":{"rendered":"

For some time I had been looking for a mutual exclusion algorithm that satisfied my complete list of desirable properties. I finally found one–the N!-bit algorithm described in this paper. The algorithm is wildly impractical, requiring N! bits of storage for N processors, but practicality was not one of my requirements. So, I decided to publish a compendium of everything I knew about the theory of mutual exclusion.<\/p>\n

The 3-bit algorithm described in this paper came about because of a visit by Michael Rabin. He is an advocate of probabilistic algorithms, and he claimed that a probabilistic solution to the mutual exclusion problem would be better than a deterministic one. I believe that it was during his brief visit that we came up with a probabilistic algorithm requiring just three bits of storage per processor. Probabilistic algorithms don’t appeal to me. (This is a question of aesthetics, not practicality.) So later, I figured out how to remove the probability and turn it into a deterministic algorithm.<\/p>\n

The first part of the paper covers the formalism for describing nonatomic operations that I had been developing since the 70s, and that is needed for a rigorous exposition of mutual exclusion. (See the discussion of [70]<\/a>.)<\/p>\n","protected":false},"excerpt":{"rendered":"

For some time I had been looking for a mutual exclusion algorithm that satisfied my complete list of desirable properties. I finally found one–the N!-bit algorithm described in this paper. The algorithm is wildly impractical, requiring N! bits of storage for N processors, but practicality was not one of my requirements. So, I decided to […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-338555","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"1986-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"313-348","msr_chapter":"","msr_isbn":"","msr_journal":"Journal 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