Abstract
Abstract interpretation-based proof carrying code uses post-fixpoints of abstract interpretations to witness that a program respects a safety policy. Some witnesses carry more information than needed and are therefore unnecessarily large. We introduce a notion of size of a witness and propose techniques for reducing the size of such certificates. For distributive analyses, we show that a smallest witness exist and we give an iterative algorithm for computing it. For non-distributive analyes we propose a technique for pruning a witness and illustrate this pruning on a relational, polyhedra-based analysis. Finally, only the existence of a witness is needed to assure the code consumer of the safety of a given program. This makes possible a compression technique of witnesses where only part of a witness is sent together with an encoding of the iterative steps necessary to prove that it is part of a post-fixpoint.
Keywords
- Convex Polyhedron
- Abstract Interpretation
- Abstract Property
- Abstract Domain
- Program Point
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Albert, E., et al.: Reduced certificates for abstraction-carrying code. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 163–178. Springer, Heidelberg (2006)
Besson, F., Jensen, T., Pichardie, D.: Proof-Carrying Code from Certified Abstract Interpretation and Fixpoint Compression. Theoretical Computer Science 364, 273–291 (2006)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximations of fixpoints. In: Proc. of the 4th ACM Symp. on Principles of Programming Languages, pp. 238–252. ACM Press, New York (1977)
Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proc. of the 5th ACM Symp. on Principles of programming languages, pp. 84–96. ACM Press, New York (1978)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Halbwachs, N.: Delay analysis in synchronous programs. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 333–346. Springer, Heidelberg (1993)
Halbwachs, N.: About synchronous programming and abstract interpretation. Science of Computer Programming 31(1), 75–89 (1998)
Koehler, H.: A contraction algorithm for finding minimal feedback sets. In: Proc. of the 28th Australasian Conf. on Computer Science, Newcastle, Australia, pp. 165–173. Australian Computer Society, Inc. (2005)
Levy, H., Low, D.W.: A contraction algorithm for finding small cycle cutsets. J. Algorithms 9(4), 470–493 (1988)
Muchnick, S.S., Jones, N.D.: Program Flow Analysis: Theory and Application. Prentice-Hall, Englewood Cliffs (1981)
Marlowe, T., Ryder, B.: Properties of data flow frameworks. Acta Informatica 28, 121–163 (1990)
Necula, G.: Proof-carrying code. In: Proc. of the 24th ACM Symp. on Principles of programming languages, pp. 106–119. ACM Press, New York (1997)
Necula, G., Lee, P.: Efficient representation and validation of proofs. In: Proc. of the 13th IEEE Symp. on Logic in Computer Science, pp. 93–104. IEEE Computer Society Press, Los Alamitos (1998)
Necula, G.C., Rahul, S.P.: Oracle-based checking of untrusted software. In: Proc. of the 28th ACM Symp. on Principles of programming languages, pp. 142–154. ACM Press, New York (2001)
Rose, E.: Lightweight bytecode verification. J. Automated Reasoning 31(3-4), 303–334 (2003)
Sankaranarayanan, S., Sipma, H., Manna, Z.: Constraint-based linear-relations analysis. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 53–68. Springer, Heidelberg (2004)
Wu, D., Appel, A.W., Stump, A.: Foundational proof checkers with small witnesses. In: Proc. of the 5th ACM Int. Conf. on Principles and Practice of Declarative Programming, pp. 264–274. ACM Press, New York (2003)
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Besson, F., Jensen, T., Turpin, T. (2007). Small Witnesses for Abstract Interpretation-Based Proofs. In: De Nicola, R. (eds) Programming Languages and Systems. ESOP 2007. Lecture Notes in Computer Science, vol 4421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71316-6_19
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DOI: https://doi.org/10.1007/978-3-540-71316-6_19
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