Abstract
Linear Relation Analysis [CH78] suffers from the cost of operations on convex polyhedra, which can be exponential with the number of involved variables. In order to reduce this cost, we propose to detect when a polyhedron is a Cartesian product of polyhedra of lower dimensions, i.e., when groups of variables are unrelated with each other. Classical operations are adapted to work on such factored polyhedra. Our implementation shows encouraging experimental results.
Vérimag is a joint laboratory of Université Joseph Fourier, CNRS and INPG associated with IMAG.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
BBC+00._N. Bjorner, A. Browne, M. Colon, B. Finkbeiner, Z. Manna, H. Sipma, and T. Uribe. Verifying temporal properties of reactive systems: A STeP tutorial. Formal Methods in System Design, 16:227–270, 2000.
N. Bjorner, I. Anca Browne, and Z. Manna. Automatic generation of invariants and intermediate assertions. Theoretical Computer Science, 173(1):49–87, February 1997.
R. Bagnara, E. Ricci, E. Zaffanella, and P. M. Hill. Possibly not closed convex polyhedra and the parma polyhedra library. In M. V. Hermenegildo and G. Puebla, editors, 9th International Symposium on Static Analysis, SAS’02, Madrid, Spain, September 2002. LNCS 2477.
P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fix-points. In 4th ACM Symposium on Principles of Programming Languages, POPL’77, Los Angeles, January 1977.
P. Cousot and N. Halbwachs. Automatic discovery of linear restraints among variables of aprogram. In 5th ACM Symposium on Principles of Programming Languages, POPL’78, Tucson (Arizona), January 1978.
N. V. Chernikova. Algorithm for discovering the set of all solutions of a linear programming problem. U.S.S.R. Computational Mathematics and Mathematical Physics, 8(6):282–293, 1968.
Ph. Clauss and V. Loechner. Parametric analysis of polyhedral iteration spaces. Journal of VLSI Signal Processing, 19(2), July 1998.
N. Dor, M. Rodeh, and M. Sagiv. Cleanness checking of string manipulations in C programs via integer analysis. In P. Cousot, editor, SAS’01, Paris, July 2001. LNCS 2126.
N. Dor, M. Rodeh, and M. Sagiv. CCSV: towards a realistic tool for statically detecting all buffer overflows in C. to appear in PLDI03, 2003.
N. Halbwachs. Détermination automatique de relations linéaires vérifiées par les variables d’un programme. Thèse de troisième cycle, University of Grenoble, March 1979.
T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. Hytech: A model checker for hybrid systems. Software Tools for Technology Transfer, 1:110–122, 1997.
N. Halbwachs, Y.E. Proy, and P. Roumanoff. Verification of real-time systems using linear relation analysis. Formal Methods in System Design, 11(2):157–185, August 1997.
F. Irigoin, P. Jouvelot, and R. Triolet. Semantical interprocedural parallelization: An overview of the PIPS project. In ACM Int. Conf. on Supercomputing, ICS’91, Köln, 1991.
B. Jeannet, N. Halbwachs, and P. Raymond. Dynamic partitioning in analyses of numerical properties. In A. Cortesi and G. Filé, editors, Static Analysis Symposium, SAS’99, Venice (Italy), September 1999. LNCS 1694, Springer Verlag.
M. Karr. Affine relationships among variables of a program. Acta Informatica, 6:133–151, 1976.
H. LeVerge. A note on Chernikova’s algorithm. RR. 635, IRISA, February 1992.
T. S. Motzkin, H. Raiffa, G. L. Thompson, and R. M. Thrall. The double description method. In H. W. Kuhn and A. W. Tucker, editors, Contribution to the Theory of Games — Volume II. Annals of Mathematic Studies, nr 28, Princeton University Press, 1953.
F. Tip. A survey of program slicing techniques. Journal of Programming Languages, 3(3):121–189, September 1995.
D. K. Wilde. A library for doing polyhedral operations. RR. 785, IRISA, December 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Halbwachs, N., Merchat, D., Parent-Vigouroux, C. (2003). Cartesian Factoring of Polyhedra in Linear Relation Analysis. In: Cousot, R. (eds) Static Analysis. SAS 2003. Lecture Notes in Computer Science, vol 2694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44898-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-44898-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40325-8
Online ISBN: 978-3-540-44898-3
eBook Packages: Springer Book Archive