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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}.

Compared with that paper we give an actual implementation of our formalised scheduling 

algorithm in C and the operating system PINTOS. Our implementation follows closely all results

we proved about optimisations of the Priority Inheritance Protocol. We are giving in this paper

more details about the proof and also surveying 

the existing literature in more depth.}

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\title{Priority Inheritance Protocol Proved Correct}

\author{Xingyuan Zhang$^1$, Christian Urban$^2$ and Chunhan Wu$^1$}

\institute{PLA University of Science and Technology, China \and 

           King's College London, United Kingdom}

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\begin{abstract}

In real-time systems with threads, resource locking and priority

sched\-uling, one faces the problem of Priority Inversion. This

problem can make the behaviour of threads unpredictable and the

resulting bugs can be hard to find.  The Priority Inheritance Protocol

is one solution implemented in many systems for solving this problem,

but the correctness of this solution has never been formally verified

in a theorem prover. As already pointed out in the literature, the

original informal investigation of the Property Inheritance Protocol

presents a correctness ``proof'' for an \emph{incorrect} algorithm. In

this paper we fix the problem of this proof by making all notions

precise and implementing a variant of a solution proposed earlier. We

also generalise the scheduling problem to the practically relevant case where

critical sections can overlap. Our formalisation in Isabelle/HOL not

just uncovers facts not mentioned in the literature, but also helps

with implementing efficiently this protocol. Earlier correct

implementations were criticised as too inefficient. Our formalisation

is based on Paulson's inductive approach to verifying protocols; our

implementation builds on top of the small PINTOS operating system used

for teaching.\medskip

{\bf Keywords:} Priority Inheritance Protocol, formal correctness proof, 

real-time systems, Isabelle/HOL

\end{abstract}

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