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\title{\bf PP \emph{Compilation Techniques for Robust Embedded Systems}} |
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\author{{\sc Ulrich Schmid}\\ |
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s@ecs.tuwien.ac.at |
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} |
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\bibliographystyle{unsrt} |
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\begin{document} |
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\maketitle |
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PP leader: \emph{Jens Knoop and Andreas Krall} |
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1.1
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1.2
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Associated researchers: \emph{} |
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1.1
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\subsubsection*{Motivation:} |
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%\emph{Informal description of the purpose of the PP (3-5 lines)} |
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Every embedded system consists of software which is written in a high |
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level language, compiled to machine language and executed on a |
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processor. For robust embedded systems new verified compilation |
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techniques are necessary to optimize for performance, power, space, |
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concurrency and reliability. |
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\subsubsection*{State of the art and related work:} |
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%\emph{Briefly describe the scientific state of the art (20-30 lines)} |
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%Compilation Techniques for Reliability |
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Because of the exponential increase of the number of transistors and |
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the continuing decrease of the feature sizes of current processors |
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soft errors mainly caused by energetic particles are becoming an |
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important design issue for robust embedded systems. Blome et |
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al.~\cite{Blome+06} observed that a majority of faults that affect the |
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architectural state of a processor come from the register file. Lee |
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and Shrivastava and proposed different solutions to cope with this |
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problem. The first assigns variables depending on their lifetime to |
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either the ECC protected or the unprotected part of a register file to |
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balance energy consumption and reliability \cite{LeeShrivastava09a}. |
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The second spills registers to ECC protected memory if the register |
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contents are not used for a long period \cite{LeeShrivastava09c}. |
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There exist complete software solutions which use different forms |
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of code duplications \cite{Reis+05}, which do failure virutalization |
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\cite{WapplerMueller08} or which use techniques like control flow |
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checking \cite{} |
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%ADL and Instruction Set Simulators \cite{MishraDutt08} |
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Compiler Verification \cite{Hoare,1328444,1314860} |
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WCET \cite{} |
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\subsubsection*{Previous achievements:} |
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%\emph{Brief description of your own contributions to the related |
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%scientific state-of-the art (5-10 lines)} |
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Jens Knoop has a long history on work on program analysis with topics |
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like partial redundancy elimination or lazy code motion |
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\cite{knoop:DSP:2008:1575,conf/cc/XueK06,scholz04}. Recently he |
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changed his research focus on worst case execution time analysis |
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\cite{SchrSchoKn09,Prantl:WLPE2008,prantl_et_al:DSP:2008:1661, |
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kirner_et_al:DSP:2008:1657,kirner_et_al:DSP:2007:1197}. He is involved |
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in the organization of many compiler conferences and since 2002 program |
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cochair of the yearly workshop on compiler optimization meets verification. |
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Andreas Krall does research in the area of architecture description |
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languages and the automatic generation of highly optimizing compilers, |
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efficient instruction set simulators and hardware from one single |
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specification of a processor \cite{BrFeKrRi09,BrEbKr07,FaKrHo07, |
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FarKrStBrand06,Krall+04micro}. An important focus is on optimization |
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techniques for embedded processors |
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\cite{EbBrSchKrWiKa08,MeKr07,PrKrHo06,HiKr03} as he lead the Christian |
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Doppler research laboratory {\em compilation techniques for embedded |
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processors} with partners from industry (Infineon, OnDemand |
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Microelectronics). |
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\subsubsection*{Goals (first 4 years):} |
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%\emph{Description of the research |
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%topics to be addressed during the first 4 years. Make sure to explicitly |
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%stress what the significant additions to the scientific knowledge are, |
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%and why they are important. (30-40 lines)} |
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New modeling and representation techniques of non-functional program and system properties on the programming and intermediate language levels |
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Definitions and measures of non-functional program and system properties (performance, time, space/memory, power, concurrency). |
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Modeling and representation of these properties alongside with the programming languages semantics |
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Adapting and enhancing state-of-the-art compilation techniques towards non-functional property and platform awareness |
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New functional and non-functional property and platform-aware compilation techniques |
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Analyses for non-functional program and system properties |
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Functional and non-functional property and platform-aware code generation techniques |
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Enabling validation and verification throughout the compilation process |
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Techniques for reducing or eliminating trusted code, annotation, etc., bases |
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\subsubsection*{Work Plan (first 4 years):} |
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%\emph{Brief description of how |
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%you intend to conduct the actual research during the first 4 years. Be sure |
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%to also describe and (coarsely) quantify the resources (staff, cost of |
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%special equipment) required for this work in a table. (20-30 lines)} |
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(1) Specification and efficient simulation of reliable processors (partial redundancy, |
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ECC, lockstep etc) and compiler optimizations to exploit/balance reliabiliy features. |
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Connection with CESAR NN1 |
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1.2
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(2) translation verification, specification of semantics of IRs solving |
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subproblems. NN1 + NN2 |
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(3) WCET NN3 |
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\begin{tabular}{llll} |
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\hline |
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{\bf Pos} & {\bf Type} & {\bf Description} & {\bf Duration} \\ |
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NN1 & PhD & reliable compilation / simulation & 4 years \\ |
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NN2 & PhD & compiler verificationi & 4 years \\ |
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NN3 & PhD & WCET & 4 years \\ |
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\hline |
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\end{tabular} |
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\subsubsection*{Goals (last 4 years):} |
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%\emph{Brief description of the |
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%eesearch topics to be addressed during the last 4 years. Make sure to |
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%explicitly stress what the significant additions to the scientific |
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%knowledge are, and why they are important. (20-30 lines)} |
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New programming languages and compilers for RESs |
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Non-functional properties and requirements as first-class language and compiler citizens |
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New compilation techniques enabling a uniform and integrated approach |
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for ensuring functional and non-functional program and system requirements |
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Replacing trust by proof |
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Certifying compilation, proof-carrying code, translation validation |
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Verified compilers, verifying compilation for RESs |
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Making legacy applications fit to and available on RESs |
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Techniques for adjusting and decompiling legacy applications |
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\subsubsection*{Collaboration with other PPs:} |
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%\emph{List the PPs you are expecting to collaborate with, and describe briefly |
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%the topic and nature of such a collaboration. (10-20 lines)} |
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\begin{itemize} |
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\item PP Composition of Non-functional Requirements [I.S.T.A./Henzinger]: |
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Links to specification and modeling of timing properties, to execution |
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models, hardware and software models. |
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\item PP Composition and Predictability in RES Architectures |
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[E182/Puschner]: Links to hard- and software models for time |
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predictable systems, verification of timing behaviour. |
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\item PP Formal Verification for Robustness [E184/Veith]: Links to software |
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model checking and testing of code (on source code and intermediate |
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code levels), support for program analysis and transformation. |
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\item PP Modeling \& Analysis of Robust Distributed Systems [E182/Schmid]: |
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Links to functional and non-functional system requirements, |
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distribution, concurrency. |
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\end{itemize} |
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\subsubsection*{External Collaborations:} |
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%\emph{List envisioned international and national collaborations, and |
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%describe briefly the topic and nature of such a collaboration. (5-10 |
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%lines)} |
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1.2
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Aviral Shrivastava, Arizona State University, Tempe, AZ, USA |
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Wolf Zimmermann, Universit\"at Halle, Halle, Germany |
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\begin{comment} |
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%Bitte hier die Bibtex-Entries einfuellen, z.B., |
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------------------------------------ |
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@article{Hoare, |
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author = {Tony Hoare}, |
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title = {The verifying compiler: A grand challenge for computing research}, |
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journal = {Journal of the ACM}, |
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volume = {50}, |
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number = {1}, |
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year = {2003}, |
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issn = {0004-5411}, |
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pages = {63--69}, |
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doi = {http://doi.acm.org/10.1145/602382.602403}, |
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publisher = {ACM}, |
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address = {New York, NY, USA}, |
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} |
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@article{1328444, |
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author = {Jean-Baptiste Tristan and Xavier Leroy}, |
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title = {Formal verification of translation validators: a case study on instruction scheduling optimizations}, |
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journal = {SIGPLAN Not.}, |
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volume = {43}, |
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number = {1}, |
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year = {2008}, |
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issn = {0362-1340}, |
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pages = {17--27}, |
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doi = {http://doi.acm.org/10.1145/1328897.1328444}, |
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publisher = {ACM}, |
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address = {New York, NY, USA}, |
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} |
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@article{1314860, |
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author = {Jan Olaf Blech and Arnd Poetzsch-Heffter}, |
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title = {A Certifying Code Generation Phase}, |
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journal = {Electron. Notes Theor. Comput. Sci.}, |
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volume = {190}, |
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number = {4}, |
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year = {2007}, |
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issn = {1571-0661}, |
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pages = {65--82}, |
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doi = {http://dx.doi.org/10.1016/j.entcs.2007.09.008}, |
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publisher = {Elsevier Science Publishers B. V.}, |
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address = {Amsterdam, The Netherlands, The Netherlands}, |
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} |
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@INPROCEEDINGS{LeeShrivastava09, |
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TITLE = {A Compiler Optimization to Reduce Soft Errors in Register Files}, |
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AUTHOR = {Jongeun Lee and Aviral Shrivastava}, |
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BOOKTITLE = {ACM SIGPLAN/SIGBED Conference on Languages, Compilers, and Tools for Embedded Systems}, |
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EDITOR = {Mahmut Kandemir}, |
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PUBLISHER = {ACM}, |
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PAGES = {??--??}, |
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ADDRESS = {Dublin}, |
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MONTH = {June}, |
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YEAR = {2009}, |
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} |
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@BOOK{MishraDutt08, |
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TITLE = {Processor Description Languages}, |
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AUTHOR = {Prabhat Mishra and Nikil Dutt (Editor)}, |
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PUBLISHER = {Morgan Kaufmann}, |
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YEAR = {2008}, |
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} |
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%Eigene Referenzen ab hier. |
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@InProceedings{SchrSchoKn09, |
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TITLE = "Adding Timing-Awareness to {AUTOSAR} Basic-Software - A Component Based Approach", |
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AUTHOR = "Dietmar Schreiner and Markus Schordan and Jens Knoop", |
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BOOKTITLE = "12th IEEE International Symposium on Object/component/service-oriented |
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Real-time distributed Computing (ISORC 2009)", |
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PUBLISHER = "IEEE", |
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ADDRESS = "Tokyo, Japan", |
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YEAR = "2009", |
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MONTH = "March", |
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PAGES = "288--292", |
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} |
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@inproceedings{Prantl:WLPE2008, |
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Address = {Udine, Italy}, |
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Author = {Adrian Prantl and Jens Knoop and Markus Schordan and Markus Triska}, |
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Booktitle = {The 18th Workshop on Logic-based methods in Programming Environments (WLPE 2008)}, |
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Month = {December 12}, |
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Title = {Constraint solving for high-level WCET analysis}, |
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Year = {2008}, |
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URL = {http://costa.tuwien.ac.at/papers/wlpe08.pdf} |
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} |
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@InProceedings{prantl_et_al:DSP:2008:1661, |
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author = "Adrian Prantl and Markus Schordan and Jens Knoop", |
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title = "TuBound - {A} Conceptually New Tool for Worst-Case |
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Execution Time Analysis", |
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booktitle = "8th Intl. Workshop on Worst-Case Execution Time (WCET) |
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Analysis", |
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year = "2008", |
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editor = "Raimund Kirner", |
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publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, |
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Germany", |
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address = "Dagstuhl, Germany", |
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URL = "http://drops.dagstuhl.de/opus/volltexte/2008/1661", |
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annote = "Keywords: Worst-case execution time (WCET) analysis, |
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Tool Chain, Flow Constraints, Source-To-Source", |
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ISBN = "978-3-939897-10-1", |
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note = "also published in print by Austrian Computer Society |
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(OCG) under ISBN 978-3-85403-237-3", |
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} |
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@InProceedings{kirner_et_al:DSP:2008:1657, |
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author = "Raimund Kirner and Albrecht Kadlec and Adrian Prantl |
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and Markus Schordan and Jens Knoop", |
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title = "Towards a Common {WCET} Annotation Language: Essential |
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Ingredients", |
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booktitle = "8th Intl. Workshop on Worst-Case Execution Time (WCET) |
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Analysis", |
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year = "2008", |
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editor = "Raimund Kirner", |
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publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, |
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Germany", |
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address = "Dagstuhl, Germany", |
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URL = "http://drops.dagstuhl.de/opus/volltexte/2008/1657", |
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annote = "Keywords: Worst-case execution time (WCET) analysis, |
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annotation languages, WCET annotation language |
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challenge", |
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ISBN = "978-3-939897-10-1", |
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note = "also published in print by Austrian Computer Society |
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(OCG) under ISBN 978-3-85403-237-3", |
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} |
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@InProceedings{kirner_et_al:DSP:2007:1197, |
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author = "Raimund Kirner and Jens Knoop and Adrian Prantl and |
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|
|
Markus Schordan and Ingomar Wenzel", |
| 322 : |
|
|
title = "{WCET} Analysis: The Annotation Language Challenge", |
| 323 : |
|
|
booktitle = "7th Intl. Workshop on Worst-Case Execution Time (WCET) |
| 324 : |
|
|
Analysis", |
| 325 : |
|
|
year = "2007", |
| 326 : |
|
|
editor = "Christine Rochange", |
| 327 : |
|
|
publisher = "Internationales Begegnungs- und Forschungszentrum |
| 328 : |
|
|
f{"u}r Informatik (IBFI), Schloss Dagstuhl, Germany", |
| 329 : |
|
|
address = "Dagstuhl, Germany", |
| 330 : |
|
|
URL = "http://drops.dagstuhl.de/opus/volltexte/2007/1197", |
| 331 : |
|
|
annote = "Keywords: Worst-case execution time analysis, WCET, |
| 332 : |
|
|
path description, annotation language challenge, |
| 333 : |
|
|
expressiveness, convenience", |
| 334 : |
|
|
} |
| 335 : |
|
|
|
| 336 : |
|
|
|
| 337 : |
|
|
@InProceedings{knoop:DSP:2008:1575, |
| 338 : |
|
|
author = {Jens Knoop}, |
| 339 : |
|
|
title = {Data-Flow Analysis for Multi-Core Computing Systems: A Reminder to Reverse Data-Flow Analysis}, |
| 340 : |
|
|
booktitle = {Scalable Program Analysis}, |
| 341 : |
|
|
year = {2008}, |
| 342 : |
|
|
editor = {Florian Martin and Hanne Riis Nielson and Claudio Riva and Markus Schordan}, |
| 343 : |
|
|
number = {08161}, |
| 344 : |
|
|
series = {Dagstuhl Seminar Proceedings}, |
| 345 : |
|
|
ISSN = {1862-4405}, |
| 346 : |
|
|
publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany}, |
| 347 : |
|
|
address = {Dagstuhl, Germany}, |
| 348 : |
|
|
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1575}, |
| 349 : |
|
|
annote = {Keywords: Multi-core computing systems, scalable program analysis, reverse data-flow analysis, demand-driven data-flow analysis} |
| 350 : |
|
|
} |
| 351 : |
|
|
|
| 352 : |
|
|
@InProceedings{conf/cc/XueK06, |
| 353 : |
|
|
title = "A Fresh Look at {PRE} as a Maximum Flow Problem", |
| 354 : |
|
|
author = "Jingling Xue and Jens Knoop", |
| 355 : |
|
|
bibdate = "2006-04-05", |
| 356 : |
|
|
bibsource = "DBLP, |
| 357 : |
|
|
http://dblp.uni-trier.de/db/conf/cc/cc2006.html#XueK06", |
| 358 : |
|
|
booktitle = "CC", |
| 359 : |
|
|
booktitle = "Compiler Construction, 15th International Conference, |
| 360 : |
|
|
{CC} 2006, Held as Part of the Joint European |
| 361 : |
|
|
Conferences on Theory and Practice of Software, {ETAPS} |
| 362 : |
|
|
2006, Vienna, Austria, March 30-31, 2006, Proceedings", |
| 363 : |
|
|
publisher = "Springer", |
| 364 : |
|
|
year = "2006", |
| 365 : |
|
|
volume = "3923", |
| 366 : |
|
|
editor = "Alan Mycroft and Andreas Zeller", |
| 367 : |
|
|
ISBN = "3-540-33050-X", |
| 368 : |
|
|
pages = "139--154", |
| 369 : |
|
|
series = "Lecture Notes in Computer Science", |
| 370 : |
|
|
URL = "http://dx.doi.org/10.1007/11688839_13", |
| 371 : |
|
|
} |
| 372 : |
|
|
|
| 373 : |
|
|
@InProceedings{scholz04, |
| 374 : |
|
|
author = "Bernhard Scholz and Nigel Horspool and Jens Knoop", |
| 375 : |
|
|
title = "Optimizing for space and time usage with speculative |
| 376 : |
|
|
partial redundancy elimination", |
| 377 : |
|
|
booktitle = "LCTES '04: Proceedings of the 2004 ACM SIGPLAN/SIGBED |
| 378 : |
|
|
conference on Languages, Compilers, and Tools for Embedded Systems", |
| 379 : |
|
|
year = "2004", |
| 380 : |
|
|
ISBN = "1-58113-806-7", |
| 381 : |
|
|
pages = "221--230", |
| 382 : |
|
|
location = "Washington, DC, USA", |
| 383 : |
|
|
publisher = "ACM Press", |
| 384 : |
|
|
} |
| 385 : |
|
|
|
| 386 : |
|
|
@InProceedings{HiKr03, |
| 387 : |
|
|
TITLE = "{VLIW} Operation Refinement for Reducing Energy Consumption", |
| 388 : |
|
|
AUTHOR = "Ulrich Hirnschrott and Andreas Krall", |
| 389 : |
|
|
BOOKTITLE = "International Symposium on System-on Chip", |
| 390 : |
|
|
PUBLISHER = "IEEE", |
| 391 : |
|
|
ADDRESS = "Tampere, Finland", |
| 392 : |
|
|
YEAR = "2003", |
| 393 : |
|
|
PAGES = "131--134", |
| 394 : |
|
|
} |
| 395 : |
|
|
|
| 396 : |
|
|
@Article{Krall+04micro, |
| 397 : |
|
|
author = {Andreas Krall and Ulrich Hirnschrott and Christian Panis and Ivan Pryanishnikov}, |
| 398 : |
|
|
title = {x{DSP}core: {A} {C}ompiler-{B}ased {C}onfigureable {D}igital {S}ignal {P}rocessor}, |
| 399 : |
|
|
journal = {IEEE Micro}, |
| 400 : |
|
|
year = {2004}, |
| 401 : |
|
|
OPTkey = {}, |
| 402 : |
|
|
volume = {24}, |
| 403 : |
|
|
number = {4}, |
| 404 : |
|
|
pages = {67-78}, |
| 405 : |
|
|
month = {July/August}, |
| 406 : |
|
|
OPTnote = {}, |
| 407 : |
|
|
OPTannote = {}, |
| 408 : |
|
|
} |
| 409 : |
|
|
|
| 410 : |
|
|
@INPROCEEDINGS{FarKrStBrand06, |
| 411 : |
|
|
TITLE = {Effective Compiler Generation by Architecture Description}, |
| 412 : |
|
|
AUTHOR = {Stefan Farfeleder and Andreas Krall and Edwin Steiner and Florian Brandner}, |
| 413 : |
|
|
BOOKTITLE = {ACM SIGPLAN/SIGBED Conference on Languages, Compilers, and Tools for Embedded Systems}, |
| 414 : |
|
|
EDITOR = {Koen De Bosschere}, |
| 415 : |
|
|
PUBLISHER = {ACM}, |
| 416 : |
|
|
PAGES = {145--152}, |
| 417 : |
|
|
ADDRESS = {Ottawa}, |
| 418 : |
|
|
MONTH = {June}, |
| 419 : |
|
|
YEAR = {2006}, |
| 420 : |
|
|
URL = {http://doi.acm.org/10.1145/1134650.1134671}, |
| 421 : |
|
|
} |
| 422 : |
|
|
|
| 423 : |
|
|
@ARTICLE{PrKrHo06, |
| 424 : |
|
|
AUTHOR = {Ivan Pryanishnikov and Andreas Krall and Nigel Horspool}, |
| 425 : |
|
|
TITLE = {Compiler Optimizations for Processors with {SIMD} Instructions}, |
| 426 : |
|
|
JOURNAL = {Software---Practice and Experience}, |
| 427 : |
|
|
PUBLISHER = {Wiley}, |
| 428 : |
|
|
VOLUME = {37}, |
| 429 : |
|
|
NUMBER = {1}, |
| 430 : |
|
|
PAGES = {93--113}, |
| 431 : |
|
|
YEAR = {2007}, |
| 432 : |
|
|
URL = {http://www3.interscience.wiley.com/cgi-bin/fulltext/112783581/PDFSTART}, |
| 433 : |
|
|
} |
| 434 : |
|
|
|
| 435 : |
|
|
@ARTICLE{FaKrHo07, |
| 436 : |
|
|
AUTHOR = {Stefan Farfeleder and Andreas Krall and Nigel Horspool}, |
| 437 : |
|
|
TITLE = {Ultra Fast Cycle-Accurate Compiled Emulation of Inorder Pipelined Architectures}, |
| 438 : |
|
|
JOURNAL = {Journal of Systems Architecture}, |
| 439 : |
|
|
PUBLISHER = {Elsevier}, |
| 440 : |
|
|
VOLUME = {53}, |
| 441 : |
|
|
NUMBER = {8}, |
| 442 : |
|
|
PAGES = {501--510}, |
| 443 : |
|
|
YEAR = {2007}, |
| 444 : |
|
|
} |
| 445 : |
|
|
|
| 446 : |
|
|
@INPROCEEDINGS{MeKr07, |
| 447 : |
|
|
TITLE = {Instruction Set Encoding Optimization for Code Size Reduction}, |
| 448 : |
|
|
AUTHOR = {Michael Med and Andreas Krall}, |
| 449 : |
|
|
BOOKTITLE = {International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation}, |
| 450 : |
|
|
ADDRESS = {Samos, Greece}, |
| 451 : |
|
|
PAGES = {9--17}, |
| 452 : |
|
|
MONTH = {July}, |
| 453 : |
|
|
YEAR = {2007} |
| 454 : |
|
|
} |
| 455 : |
|
|
|
| 456 : |
|
|
@INPROCEEDINGS{BrEbKr07, |
| 457 : |
|
|
TITLE = {Compiler Generation from Structural Architecture Descriptions}, |
| 458 : |
|
|
AUTHOR = {Florian Brandner and Dietmar Ebner and Andreas Krall}, |
| 459 : |
|
|
BOOKTITLE = {International Conference on Compilers, Architecture, and Synthesis for Embedded Systems}, |
| 460 : |
|
|
ADDRESS = {Salzburg, Austria}, |
| 461 : |
|
|
PAGES = {13--22}, |
| 462 : |
|
|
MONTH = {September}, |
| 463 : |
|
|
YEAR = {2007} |
| 464 : |
|
|
} |
| 465 : |
|
|
|
| 466 : |
|
|
@INPROCEEDINGS{EbBrSchKrWiKa08, |
| 467 : |
|
|
TITLE = {Generalized Instruction Selection using {SSA}-Graphs}, |
| 468 : |
|
|
AUTHOR = {Dietmar Ebner and Florian Brandner and Bernhard Scholz and Andreas Krall and Peter Wiedermann and Albrecht Kadlec}, |
| 469 : |
|
|
BOOKTITLE = {ACM SIGPLAN/SIGBED Conference on Languages, Compilers, and Tools for Embedded Systems}, |
| 470 : |
|
|
EDITOR = {John Regehr}, |
| 471 : |
|
|
PUBLISHER = {ACM}, |
| 472 : |
|
|
PAGES = {31--40}, |
| 473 : |
|
|
ADDRESS = {Tucson}, |
| 474 : |
|
|
MONTH = {June}, |
| 475 : |
|
|
YEAR = {2008}, |
| 476 : |
|
|
} |
| 477 : |
|
|
|
| 478 : |
|
|
@INPROCEEDINGS{BrFeKrRi09, |
| 479 : |
|
|
TITLE = {Fast and Accurate Simulation using the LLVM Compiler Framework}, |
| 480 : |
|
|
AUTHOR = {Florian Brandner and Andreas Fellnhofer and Andreas Krall and David Riegler}, |
| 481 : |
|
|
BOOKTITLE = {Rapid Simulation and Performance Evaluation: Methods and Tools (RAPIDO'09)}, |
| 482 : |
|
|
EDITOR = {Smail Niar, Rainer Leupers, Olivier Temam}, |
| 483 : |
|
|
PUBLISHER = {HiPEAC}, |
| 484 : |
|
|
PAGES = {1--6}, |
| 485 : |
|
|
ADDRESS = {Paphos, Cyprus}, |
| 486 : |
|
|
MONTH = {January}, |
| 487 : |
|
|
YEAR = {2009}, |
| 488 : |
|
|
} |
| 489 : |
|
|
\end{comment} |
| 490 : |
|
|
|
| 491 : |
|
|
\bibliography{res} % Input von res.bib, kommt dann spaeter dazu ... |
| 492 : |
|
|
|
| 493 : |
|
|
\end{document} |