source: Papers/jar-cerco-2017/cerco.tex @ 3645

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65
66\title{CerCo: Certified Complexity\thanks{The project CerCo acknowledges the
67financial support of the Future and Emerging Technologies (FET) programme within
68the Seventh Framework Programme for Research of the European Commission, under
69FET-Open grant number: 243881}}
70\subtitle{Source-level complexity analysis for a large fragment of C}
71\journalname{Journal of Automated Reasoning}
72\titlerunning{Certified Complexity}
73\date{Received: date / Accepted: date}
74\author{Jaap Boender \and Brian Campbell \and Dominic P. Mulligan \and Claudio Sacerdoti~Coen
75        \and %Roberto
76Roberto~M. Amadio \and
77Nicolas Ayache \and
78Fran\c{c}ois Bobot \and
79Ilias Garnier \and
80Antoine Madet \and
81James McKinna \and
82Mauro Piccolo \and
83Randy Pollack \and
84Yann R\'{e}gis-Gianas \and
85Ian Stark \and
86Paolo Tranquilli} % who else?
87\authorrunning{Boender, Campbell, Mulligan, and Sacerdoti~Coen}
88\institute{Roberto M. Amadio, Antoine Madet, and Yann R\'{e}gis-Gianas \at
89            Universit\'e Paris Diderot (Paris 7), Paris, France.
90           \and
91           Nicolas Ayache \at
92            IKOS Consulting, France.
93           \and
94           Fran\c{c}ois Bobot \at
95           Software Reliability Laboratory, CEA, France.
96           \and
97           Jaap Boender \at
98              Middlesex University London, United Kingdom.
99           \and
100           Brian Campbell, James McKinna, Randy Pollack, and Ian Stark \at
101              University of Edinburgh, United Kingdom.
102           \and
103           Ilias Garnier, \at
104             \'Ecole Normale Sup\'erieure, Paris, France.
105           \and
106           Dominic P. Mulligan \at
107             University of Cambridge, United Kingdom.
108           \and
109           Claudio Sacerdoti~Coen \at
110              University of Bologna, Italy.}
111
112\begin{document}
113
114\maketitle
115
116\begin{abstract}
117Concrete non-functional properties of programs---for example, time and space usage as measured in basal units of measure such as milliseconds and bytes allocated---are important components of the specification of a program, and therefore overall program correctness.
118Indeed, for many application domains, concrete complexity analysis is arguably more important than any asymptotic complexity analysis.
119Libraries exporting cryptographic primitives that must be impervious to timing side-channel attacks, or real-time applications with hard timing limits on responsiveness, are examples.
120
121Worst Case Execution Time tools, based on abstract interpretation, currently represent the state-of-the-art in determining concrete time bounds for a program execution.
122These tools suffer from a number of disadvantages, not least the fact that all analysis is performed on machine code, rather than high-level source code, making results hard to interpret by programmers.
123Further, these tools are often complex pieces of software, whose analysis is hard to trust.
124More ideal would be a mechanism to `lift' a cost model from the machine code generated by a compiler, back to the source code level, where analyses could be performed in terms understood by the programmer.
125How one could incorporate the precision of traditional static analyses into such a high-level approach---and how this could be done reliably---is not \emph{a priori} clear.
126
127In this paper, we describe the scientific contributions of the European Union's FET-Open Project CerCo (`Certified Complexity').
128CerCo's main achievement is the development of a technique for analysing non-functional properties of programs at the source level, with little or no loss of accuracy, and a small trusted code base.
129The core component of the project is a compiler for a large fragment of the C programming language, verified in the Matita theorem prover, that produces an instrumented copy of the source code in addition to generating object code.
130This instrumentation exposes, and tracks precisely, the concrete (non-asymptotic) computational cost of the input program at the source level.
131Untrusted invariant generators and trusted theorem provers may then be used to compute and certify the parametric execution time of the code.
132
133We describe the architecture of our C compiler, its proof of correctness, and the associated toolchain developed around the compiler.
134Using our toolchain, we describe a case study in applying our technique to the verification of concrete timing bounds for cryptographic code.
135
136\keywords{Verified compilation \and Complexity analysis \and Worst Case Execution Time analysis \and CerCo (`Certified Complexity') \and Matita}
137\end{abstract}
138
139\include{introduction}
140\include{architecture}
141\include{proof}
142\include{development}
143\include{framac}
144\include{conclusions}
145
146\begin{acknowledgements}
147\end{acknowledgements}
148
149\bibliographystyle{spmpsci}
150\bibliography{cerco}
151
152\end{document}
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