Abstract
Linear equalities, disequalities and inequalities on fixed-width bit-vectors, collectively called linear modular constraints, form an important fragment of the theory of fixed-width bit-vectors. We present an efficient and bit-precise algorithm for quantifier elimination from conjunctions of linear modular constraints. Our algorithm uses a layered approach, whereby sound but incomplete and cheaper layers are invoked first, and expensive but complete layers are called only when required. We have extended the above algorithm to work with boolean combinations of linear modular constraints as well. Experiments on an extensive set of benchmarks demonstrate that our techniques significantly outperform alternative quantifier elimination techniques based on bit-blasting and Presburger Arithmetic.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
John, A.K., Chakraborty, S.: A quantifier elimination algorithm for linear modular equations and disequations. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 486–503. Springer, Heidelberg (2011)
John, A.K., Chakraborty, S.: Extending quantifier elimination to linear inequalities on bit-vectors. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 78–92. Springer, Heidelberg (2013)
Bjørner, N., Blass, A., Gurevich, Y., Musuvathi, M.: Modular difference logic is hard. CoRR abs/0811.0987 (2008)
Kroening, D., Strichman, O.: Decision procedures: an algorithmic point of view. Texts in Theoretical Computer Science. Springer (2008)
Chaki, S., Gurfinkel, A., Strichman, O.: Decision diagrams for linear arithmetic. In: FMCAD 2009 (2009)
Pugh, W.: The Omega Test: A fast and practical integer programming algorithm for dependence analysis. Communications of the ACM, 102–114 (1992)
Monniaux, D.: A quantifier elimination algorithm for linear real arithmetic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 243–257. Springer, Heidelberg (2008)
Ganesh, V., Dill, D.L.: A decision procedure for bit-vectors and arrays. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 519–531. Springer, Heidelberg (2007)
Muller-Olm, M., Seidl, H.: Analysis of modular arithmetic. ACM Transactions on Programming Languages and Systems 29(5), 29 (2007)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers C-35(8), 677–691 (1986)
CUDD release 2.4.2 website, vlsi.colorado.edu/fabio/CUDD
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
John, A.K., Chakraborty, S. (2014). Quantifier Elimination for Linear Modular Constraints. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_46
Download citation
DOI: https://doi.org/10.1007/978-3-662-44199-2_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
Online ISBN: 978-3-662-44199-2
eBook Packages: Computer ScienceComputer Science (R0)