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<title data-rh="true">What is the Byzantine Generals Problem in Distributed Systems?</title>
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aria-label="Post UFI" role="region" class="pencraft pc-display-flex pc-flexDirection-column pc-paddingBottom-16 pc-reset"><div class="pencraft pc-display-flex pc-paddingTop-16 pc-paddingBottom-16 pc-justifyContent-space-between pc-alignItems-center pc-reset"><div class="pencraft pc-display-flex pc-gap-12 pc-alignItems-center pc-reset byline-wrapper"><div class="pencraft pc-display-flex pc-flexDirection-column pc-reset"><div class="pencraft pc-display-flex pc-gap-4 pc-reset"><div class="pencraft pc-reset color-secondary-ls1g8s line-height-20-t4M0El font-meta-MWBumP size-11-NuY2Zx weight-medium-fw81nC transform-uppercase-yKDgcq reset-IxiVJZ meta-EgzBVA"><time datetime="2025-01-31T22:31:03.575Z" title="2025-01-31T22:31:03.575Z">Jan 31, 2025</time></div></div></div></div></div><div class="pencraft pc-display-flex pc-gap-16 pc-justifyContent-space-between pc-alignItems-center pc-reset flex-grow-rzmknG post-ufi"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><div class="like-button-container post-ufi-button style-button"><button tabindex="0" type="button" aria-label="Like (32)" aria-pressed="false" class="pencraft pc-reset pencraft post-ufi-button style-button has-label with-border"><svg aria-hidden="true" style="height:20px;width:20px;" width="20" height="20" viewBox="0 0 24 24" fill="#000000" stroke-width="2" stroke="#000" xmlns="http://www.w3.org/2000/svg" class="icon"><g><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-heart"><path d="M19 14c1.49-1.46 3-3.21 3-5.5A5.5 5.5 0 0 0 16.5 3c-1.76 0-3 .5-4.5 2-1.5-1.5-2.74-2-4.5-2A5.5 5.5 0 0 0 2 8.5c0 2.3 1.5 4.05 3 5.5l7 7Z"></path></svg></g></svg><div class="label">32</div></button></div><button tabindex="0" type="button" aria-label="View comments (0)" data-href="https://newsletter.scalablethread.com/p/what-is-the-byzantine-generals-problem/comments" class="pencraft pc-reset pencraft post-ufi-button style-button post-ufi-comment-button no-label with-border"><svg aria-hidden="true" style="height:20px;width:20px;" width="20" height="20" viewBox="0 0 24 24" fill="#000000" stroke-width="2" stroke="#000" xmlns="http://www.w3.org/2000/svg" class="icon"><g><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-message-circle"><path d="M7.9 20A9 9 0 1 0 4 16.1L2 22Z"></path></svg></g></svg></button><button tabindex="0" type="button" id="radix-P0-24" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="pencraft pc-reset pencraft post-ufi-button style-button has-label with-border"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="2" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg" class="icon"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg><div class="label">6</div></button></div><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft post-ufi-button style-button has-label with-border"><div class="label">Share</div></button></div></div></div></div><div class="visibility-check"></div><div><div class="dt-post-body"><div class="available-content"><div dir="auto" class="body markup"><p>The Byzantine Generals Problem is a thought experiment in distributed computing to understand the challenges of reaching a consensus when some nodes may be untrustworthy or unreliable (node behavior). It shows how difficult it can be to coordinate actions when some system members may act dishonestly.</p><h2 class="header-anchor-post">The Byzantine Generals Problem<div class="pencraft pc-display-flex pc-alignItems-center pc-position-absolute pc-reset header-anchor-parent"><div class="pencraft pc-display-contents pc-reset pubTheme-yiXxQA"><div id="§the-byzantine-generals-problem" class="pencraft pc-reset header-anchor offset-top"></div><button tabindex="0" type="button" aria-label="Link" data-href="https://newsletter.scalablethread.com/i/154559673/the-byzantine-generals-problem" class="pencraft pc-reset pencraft iconButton-mq_Et5 iconButtonBase-dJGHgN buttonBase-GK1x3M buttonStyle-r7yGCK size_sm-G3LciD priority_secondary-S63h9o"><svg xmlns="http://www.w3.org/2000/svg" width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></button></div></div></h2><p><span>Imagine three or more generals surrounding a city they want to capture. They need to agree on one action: attack or retreat. They can only communicate through messengers. Unlike </span><a href="https://newsletter.scalablethread.com/p/what-is-the-two-generals-problem">the two generals problem</a><span>, the messages will be delivered correctly this time. However, one or more generals could be &quot;traitors&quot; who send false or confusing messages. The honest generals cannot ignore a suspected traitor's message because they don't know who the traitors are. The goal is for all honest generals to agree on the same plan: attack or retreat. For example, if General C receives two contradicting messages—one from General A saying to attack and another from General B saying General A ordered a retreat—General C cannot tell if General B is lying or if General A is giving false information.</span></p><div class="captioned-image-container"><figure><a target="_blank" href="https://substackcdn.com/image/fetch/$s_!-sbc!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png" data-component-name="Image2ToDOM" class="image-link image2 is-viewable-img can-restack"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!-sbc!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 424w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 848w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 1272w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 1456w" sizes="100vw"/><img src="https://substackcdn.com/image/fetch/$s_!-sbc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png" width="1456" height="2259" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:2259,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:475993,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:&quot;image/png&quot;,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:true,&quot;internalRedirect&quot;:null,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" alt srcset="https://substackcdn.com/image/fetch/$s_!-sbc!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 424w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 848w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 1272w, https://substackcdn.com/image/fetch/$s_!-sbc!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F46d3960e-49ce-4236-aa64-618dca44e42b_2520x3910.png 1456w" sizes="100vw" fetchpriority="high" class="sizing-normal"/></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg aria-hidden="true" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption">Fig. In both scenarios, it's not possible for General C to know which other General is lying</figcaption></figure></div><h2 class="header-anchor-post">Node Behavior in Distributed Systems<div class="pencraft pc-display-flex pc-alignItems-center pc-position-absolute pc-reset header-anchor-parent"><div class="pencraft pc-display-contents pc-reset pubTheme-yiXxQA"><div id="§node-behavior-in-distributed-systems" class="pencraft pc-reset header-anchor offset-top"></div><button tabindex="0" type="button" aria-label="Link" data-href="https://newsletter.scalablethread.com/i/154559673/node-behavior-in-distributed-systems" class="pencraft pc-reset pencraft iconButton-mq_Et5 iconButtonBase-dJGHgN buttonBase-GK1x3M buttonStyle-r7yGCK size_sm-G3LciD priority_secondary-S63h9o"><svg xmlns="http://www.w3.org/2000/svg" width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></button></div></div></h2><p><span>In distributed systems, Generals represent the nodes or processes involved. Messages are the communications that happen between these nodes. Traitors are faulty or malicious nodes, known as </span><em>Byzantine nodes</em><span>, that may send incorrect or false information. Consensus is the agreement that all working nodes must reach a single value or action (an agreement). </span></p><p>A Byzantine node can behave in unpredictable ways. It might send different messages to different nodes, fake messages, or fail to send messages altogether. This is similar to a general who spreads lies and tries to mess up communication. For example, in a blockchain network, nodes must agree on the order of transactions. A malicious node might try to spread false transactions or mess with the consensus process, risking the integrity of the blockchain.</p><h2 class="header-anchor-post">3f + 1 Rule<div class="pencraft pc-display-flex pc-alignItems-center pc-position-absolute pc-reset header-anchor-parent"><div class="pencraft pc-display-contents pc-reset pubTheme-yiXxQA"><div id="§3f-1-rule" class="pencraft pc-reset header-anchor offset-top"></div><button tabindex="0" type="button" aria-label="Link" data-href="https://newsletter.scalablethread.com/i/154559673/3f-1-rule" class="pencraft pc-reset pencraft iconButton-mq_Et5 iconButtonBase-dJGHgN buttonBase-GK1x3M buttonStyle-r7yGCK size_sm-G3LciD priority_secondary-S63h9o"><svg xmlns="http://www.w3.org/2000/svg" width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></button></div></div></h2><p>The Byzantine Generals Problem has an important limitation: it is impossible to reach an agreement if more than one-third of the participants are faulty. This is the &quot;3f+1&quot; rule, where 'f' is the number of faulty nodes. In simpler terms, if there are 'f' faulty nodes, there must be at least 2f + 1 loyal nodes. This way, even if the faulty nodes team up to share wrong information, the loyal nodes will still have a majority and can reach an agreement.</p><p>For example, if we expect at most one faulty node (f=1), we need at least four nodes (3*1 + 1 = 4) in the system. With four nodes, even if one is faulty, the remaining three loyal nodes can vote against the faulty one and reach a consensus.</p><h2 class="header-anchor-post">References<div class="pencraft pc-display-flex pc-alignItems-center pc-position-absolute pc-reset header-anchor-parent"><div class="pencraft pc-display-contents pc-reset pubTheme-yiXxQA"><div id="§references" class="pencraft pc-reset header-anchor offset-top"></div><button tabindex="0" type="button" aria-label="Link" data-href="https://newsletter.scalablethread.com/i/154559673/references" class="pencraft pc-reset pencraft iconButton-mq_Et5 iconButtonBase-dJGHgN buttonBase-GK1x3M buttonStyle-r7yGCK size_sm-G3LciD priority_secondary-S63h9o"><svg xmlns="http://www.w3.org/2000/svg" width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></button></div></div></h2><ul><li><p><span>Martin Kleppmann. (2020, October 28). </span><em>Distributed Systems 2.2: The Byzantine generals problem</em><span> [Video]. YouTube. </span><a href="https://www.youtube.com/watch?v=LoGx_ldRBU0">https://www.youtube.com/watch?v=LoGx_ldRBU0</a></p></li></ul><div><hr/></div><p><em>If you enjoyed this article, please hit the ❤️ like button.</em></p><p><em>If you think someone else will benefit from this, then please 🔁 share this post.</em></p></div></div><div class="visibility-check"></div></div><div class="post-footer"><div class="pencraft pc-display-flex pc-gap-16 pc-paddingTop-16 pc-paddingBottom-16 pc-justifyContent-space-between pc-alignItems-center pc-reset flex-grow-rzmknG border-top-detail-themed-k9TZAY border-bottom-detail-themed-Ua9186 post-ufi"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><div class="like-button-container post-ufi-button style-button"><button tabindex="0" type="button" aria-label="Like (32)" aria-pressed="false" class="pencraft pc-reset pencraft post-ufi-button style-button has-label with-border"><svg aria-hidden="true" style="height:20px;width:20px;" width="20" height="20" 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class=\\\"lucide lucide-maximize2 lucide-maximize-2\\\"><polyline points=\\\"15 3 21 3 21 9\\\"></polyline><polyline points=\\\"9 21 3 21 3 15\\\"></polyline><line x1=\\\"21\\\" x2=\\\"14\\\" y1=\\\"3\\\" y2=\\\"10\\\"></line><line x1=\\\"3\\\" x2=\\\"10\\\" y1=\\\"21\\\" y2=\\\"14\\\"></line></svg></button></div></div></div></a><figcaption class=\\\"image-caption\\\">Fig. In both scenarios, it's not possible for General C to know which other General is lying</figcaption></figure></div><h2>Node Behavior in Distributed Systems</h2><p>In distributed systems, Generals represent the nodes or processes involved. Messages are the communications that happen between these nodes. Traitors are faulty or malicious nodes, known as <em>Byzantine nodes</em>, that may send incorrect or false information. Consensus is the agreement that all working nodes must reach a single value or action (an agreement). </p><p>A Byzantine node can behave in unpredictable ways. It might send different messages to different nodes, fake messages, or fail to send messages altogether. This is similar to a general who spreads lies and tries to mess up communication. For example, in a blockchain network, nodes must agree on the order of transactions. A malicious node might try to spread false transactions or mess with the consensus process, risking the integrity of the blockchain.</p><h2>3f + 1 Rule</h2><p>The Byzantine Generals Problem has an important limitation: it is impossible to reach an agreement if more than one-third of the participants are faulty. This is the \\\"3f+1\\\" rule, where 'f' is the number of faulty nodes. In simpler terms, if there are 'f' faulty nodes, there must be at least 2f + 1 loyal nodes. This way, even if the faulty nodes team up to share wrong information, the loyal nodes will still have a majority and can reach an agreement.</p><p>For example, if we expect at most one faulty node (f=1), we need at least four nodes (3*1 + 1 = 4) in the system. With four nodes, even if one is faulty, the remaining three loyal nodes can vote against the faulty one and reach a consensus.</p><h2>References</h2><ul><li><p>Martin Kleppmann. (2020, October 28). <em>Distributed Systems 2.2: The Byzantine generals problem</em> [Video]. YouTube. <a href=\\\"https://www.youtube.com/watch?v=LoGx_ldRBU0\\\">https://www.youtube.com/watch?v=LoGx_ldRBU0</a></p></li></ul><div><hr></div><p><em>If you enjoyed this article, please hit the \u2764\uFE0F like button.</em></p><p><em>If you think someone else will benefit from this, then please \uD83D\uDD01 share this post.</em></p>\",\"has_dynamic_content\":false,\"truncated_body_text\":\"The Byzantine Generals Problem is a thought experiment in distributed computing to understand the challenges of reaching a consensus when some nodes may be untrustworthy or unreliable (node behavior). 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