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%%%\titlerunning{Proving the Priority Inheritance Protocol Correct}+
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\begin{document}+
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\footnotetext[1]{This paper is a revised, corrected and expanded version of \cite{ZhangUrbanWu12}.+
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Compared with that paper we give an actual implementation of our formalised scheduling +
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algorithm in C and the operating system PINTOS. Our implementation follows closely all results+
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we proved about optimisations of the Priority Inheritance Protocol.}+
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\title{Priority Inheritance Protocol Proved Correct}+
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\author{Xingyuan Zhang$^1$, Christian Urban$^2$ and Chunhan Wu$^1$}+
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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. We also generalise the original informal proof to the+
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practically relevant case where critical sections can+
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overlap. Our formalisation in Isabelle/HOL not just+
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uncovers facts not mentioned in the literature, but also helps with+
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implementing efficiently 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; our implementation+
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builds on top of the small PINTOS operating system used for teaching.\medskip+
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%{\bf Keywords:} Priority Inheritance Protocol, formal correctness proof, +
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%real-time systems, Isabelle/HOL+
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\end{abstract}+
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\end{document}+
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