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The work formulates path criticality and reduces its computation to evaluating a multivariate normal CDF, enabling consistent handling of non-idealities. It extends edge criticality computation using the same CDF framework and introduces an analytic conditioning method that improves accuracy while remaining substantially faster than conventional numerical integration and Monte Carlo approaches.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/path-criticality-computation-in-parameterized-statistical-timing-analysis/239476/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/path-criticality-computation-in-parameterized-statistical-timing-analysis/239476.png","ImageObject",442,249,{"name":88,"@type":89},"Tawan","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-30","2026-09-11",true,{"@type":98,"interactionType":99,"userInteractionCount":15},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What does path criticality measure in SSTA?","Question",{"text":108,"@type":109},"Path criticality is defined as the probability that a given path becomes the critical path.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What does edge criticality measure in SSTA?",{"text":113,"@type":109},"Edge criticality is defined as the probability that the edge lies on the critical path.",{"name":115,"@type":106,"acceptedAnswer":116},"How is the proposed path criticality computation performed efficiently?",{"text":117,"@type":109},"The computation is reduced to evaluating a multivariate normal CDF, then a novel analytic conditioning operation is used to improve accuracy compared with max-based approximations while greatly reducing runtime versus Monte Carlo sampling.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},239476,1789149464,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":15,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":125,"read_time":140},2336475104042,"https://ap-avatar.wpscdn.com/avatar/22000c4c32af1715be0?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786537525561427321","Path Criticality Computation in Parameterized  \nStatistical Timing Analysis  \nJaeyong Chung, Jinjun Xiong*, Vladimir Zolotov*, and Jacob A. Abraham  \nComputer Engineering Research Center, University of Texas at Austin  \n*IBM T.J. Waston Research Center, Yorktown Heights  \nOutline  \n􀂃 Introduction  \n􀂃 Path criicality formulation  \n􀂃 P ( I A k \u003C Bk ) i = 1  \n􀂃 A novel method to compute a joint probability in SSTA  \n􀂃 Conclusions  \nIntroduction  \n􀂃 In SSTA, criticality is a representative metric to gauge how important a given edge or path is in terms of timing  \n􀂃 The criticality of a path is defined as the probability that the path becomes the critical path  \n􀂃 The criticality of an edge is defined as the probability that the edge is on the critical path  \nIntroduction  \n􀂃 Criticality is used in timing/yield optimization  \n􀂃 Gate sizing, buffer insertion, Vth assignment  \n􀂃 Transistor sizing  \n􀂃 Criticality is also very useful in testing  \n􀂃 Timing critical paths (i.e. , paths with high path criticality values) can be selected using SSTA  \n􀂃 An ATPG tool takes these paths and generates test patterns sensitizing them  \n􀂃 These patterns can be employed in performance testing, SDD testing, and speed-binning  \nPrevious Work  \n􀂃 Run SSTA  \n􀂃 Obtain the circuit slack Sc  \n􀂃 Obtain the slack S(p 1 ) of a given path p 1  \n􀂃 Compute P ( S ( p1 ) \u003C Sc )  \nSc = min{S ( p 1 ), S ( p 2 ), S ( p 3 ),... }  \nXiong et al, Incremental criticality and yield gradients, DATE 2008  \nPrevious Work  \n􀂃 The complement slack of a path is the minimum of all path slacks in the circuit excluding the path slack  \n􀂃 Obtain the complement slack  S  ( p1 ) from S ( p1 ), Sc  \n􀂃 Compute P ( S ( p1 ) \u003C  S  ( p1 )) S ( p 1 ) = min{S ( p 2 ), S ( p 3 ),... }  \nLots of information is captured by a too simple linear form  \nXiong et al, Incremental criticality and yield gradients, DATE 2008  \nGeneral path criticality formulation  \n􀂃 Partition the set of all paths in the circuit into m groups  \n􀂃 Compute the minimum path slack of each group  \n􀂃 Path criticality of p 1 can be written as  \nm  \nP ( IS ( p1 ) \u003C Si )  \ni = 1  \n1 . Various ways to formulate path criticality  \n2 . Smart formulation considering non-idealities of SSTA can reduce errors  \nPartitioning  \nP (( V +W  \n> max {X +W , Y +W })I ( V + W > Z ))  \n= P (( V +W > max {X, Y } + W) I ( V + W > Z )) distributivity  \n= P (( V > max{X, Y })I ( V +W > Z ))  \nComputing a joint probability  \n􀂃 Path criticality computation is reduced to evaluating the multivariate normal CDF  \nm m  \nP ( I A k \u003C Bk ) = P ( I A k − Bk \u003C 0 )  \ni = 1 i = 1  \n= Φ (x1 , x 2 , ..., x m )  \n􀂃 Edge criticality computation is also reduced to the  \nsame problem A path criticality  \nAn edge criticality  \nA new way to evaluate the CDF  \n􀂃 Previous approaches to evaluate the CDF  \n􀂃 Numerical Integration (e.g., mvncdf in matlab)  \n􀂃 Accurate but extremely slow  \n􀂃 Monte Carlo sampling (slow)  \n􀂃 Using the max operation provided by SSTA  \n􀂃 Very fast but poor accuracy  \n􀂃 We propose a novel, analytic conditioning operation  \n􀂃 1000x faster than Monte Carlo sampling at the same accuracy  \n􀂃 2~3x accurate at the cost of 3~4x runtime compared to max operation 10","cbCaitDYyux51bnm","https://ap.wps.com/l/cbCaitDYyux51bnm","pdf",302471,24,"English","# Introduction\n## Criticality in SSTA (path and edge definitions)\n## Applications in optimization and testing\n# Previous Work\n## Incremental criticality and yield gradients\n## Complement slack formulation\n# General Path Criticality Formulation\n## Partitioning paths and probability expression\n## Smart formulations under SSTA non-idealities\n# Computing a Joint Probability via Multivariate Normal CDF\n## Reducing path criticality computation\n## Edge criticality using the same framework\n# A New Way to Evaluate the CDF\n## Limitations of numerical integration and Monte Carlo\n## Max-based approximation tradeoffs\n## Proposed analytic conditioning method\n# Conclusions","[{\"question\":\"What does path criticality measure in SSTA?\",\"answer\":\"Path criticality is defined as the probability that a given path becomes the critical path.\"},{\"question\":\"What does edge criticality measure in SSTA?\",\"answer\":\"Edge criticality is defined as the probability that the edge lies on the critical path.\"},{\"question\":\"How is the proposed path criticality computation performed efficiently?\",\"answer\":\"The computation is reduced to evaluating a multivariate normal CDF, then a novel analytic conditioning operation is used to improve accuracy compared with max-based approximations while greatly reducing runtime versus Monte Carlo sampling.\"}]","Path Criticality Computation in Parameterized Statistical Timing Analysis | PDF",8]