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\documentclass[runningheads]{llncs}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{mathpartir}
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%\usepackage{tikz}
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%\usepackage{pgf}
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%\usetikzlibrary{arrows,automata,decorations,fit,calc}
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%\usetikzlibrary{shapes,shapes.arrows,snakes,positioning}
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%\usepgflibrary{shapes.misc} % LATEX and plain TEX and pure pgf
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%\usetikzlibrary{matrix}
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\usepackage{pdfsetup}
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\usepackage{ot1patch}
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\usepackage{times}
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%%\usepackage{proof}
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%%\usepackage{mathabx}
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\usepackage{stmaryrd}
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\usepackage{url}
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\titlerunning{Proving the Priority Inheritance Protocol Correct}
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\urlstyle{rm}
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\isabellestyle{it}
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\renewcommand{\isastyleminor}{\it}%
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\renewcommand{\isastyle}{\normalsize\it}%
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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\renewcommand{\isasymequiv}{$\dn$}
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\renewcommand{\isasymemptyset}{$\varnothing$}
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\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
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\newcommand{\isasymcalL}{\ensuremath{\cal{L}}}
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\newcommand{\isasymbigplus}{\ensuremath{\bigplus}}
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\newcommand{\bigplus}{\mbox{\Large\bf$+$}}
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\begin{document}
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\title{Priority Inheritance Protocol Proved Correct}
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\author{Xingyuan Zhang\inst{1} \and Christian Urban\inst{2} \and Chunhan Wu\inst{1}}
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\institute{PLA University of Science and Technology, China \and
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King's College London, United Kingdom}
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\maketitle
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\begin{abstract}
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In real-time systems with threads, resource locking and
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priority sched\-uling, one faces the problem of Priority
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Inversion. This problem can make the behaviour of threads
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unpredictable and the resulting bugs can be hard to find. The
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Priority Inheritance Protocol is one solution implemented in many
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systems for solving this problem, but the correctness of this solution
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has never been formally verified in a theorem prover. As already
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pointed out in the literature, the original informal investigation of
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the Property Inheritance Protocol presents a correctness ``proof'' for
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an \emph{incorrect} algorithm. In this paper we fix the problem of
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this proof by making all notions precise and implementing a variant of
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a solution proposed earlier. Our formalisation in Isabelle/HOL
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uncovers facts not mentioned in the literature, but also shows how to
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efficiently implement this protocol. Earlier correct implementations
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were criticised as too inefficient. Our formalisation is based on
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Paulson's inductive approach to verifying protocols.\medskip
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{\bf Keywords:} Priority Inheritance Protocol, formal connectness proof,
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real-time systems, Isabelle/HOL
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\end{abstract}
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\input{session}
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\bibliographystyle{plain}
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\bibliography{root}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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