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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{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{Myhill-Nerode using Regular Expressions}
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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{A Formalisation of Priority Inheritance Protocol \\
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for Correct and Efficient Implementation}
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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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262
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\maketitle
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\begin{abstract}
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267
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In realtime systems with support for resource locking and processes
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involving priorities, one faces the problem of priority
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inversion. This problem can make the behaviour of processes
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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 description of the
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Property Inheritance Protocol presents an informal correctness
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``proof'' for an \emph{incorrect} algorithm. In this paper we fix the
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problem of the original proof by making all notions precise and
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implementing a variant of a solution proposed earlier. Our
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formalisation in Isabelle/HOL uncovered facts not mentioned in the
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literature, but also shows how to efficiently implement this
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protocol. Earlier correct implementations were criticised as too
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inefficient. Our formalisation is based on Paulson's inductive
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approach to verifying protocols.\medskip
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265
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{\bf Keywords:} Priority Inheritance Protocol, formal connectness proof,
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realtime systems
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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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