Abstract
This paper focuses on bounded invariant checking for partially specified circuits – designs containing so-called blackboxes – using the well known 01X- and QBF-encoding techniques. For detecting counterexamples, modeling the behavior of a blackbox using 01X-encoding is fast, but rather coarse as it limits what problems can be verified. We introduce the idea of 01X-hardness, mainly the classification of problems for which this encoding technique does not provide any useful information about the existence of a counterexample. Furthermore, we provide a proof for 01X-hardness based on Craig interpolation, and show how the information contained within the Craig interpolant or unsat-core can be used to determine heuristically which blackbox outputs to model in a more precise way. We then compare 01X, QBF and multiple hybrid modeling methods. Finally, our total workflow along with multiple state-of-the-art QBF-solvers are shown to perform well on a range of industrial blackbox circuit problems.
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.
References
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Clarke, E., Biere, A., Raimi, R., Zhu, Y.: Bounded Model Checking Using Satisfiability Solving. Formal Methods in System Design 19, 7–34 (2001)
Craig, W.: Linear Reasoning: A New Form of the Herbrand-Gentzen Theorem. Journal of Symbolic Logic 22(3), 250–268 (1957)
Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas. Journal of Artificial Intelligence Research (JAIR) 26, 371–416 (2006)
Herbstritt, M., Becker, B.: On SAT-based Bounded Invariant Checking of Blackbox Designs. In: Microprocessor Test and Verification Workshop (MTV), pp. 23–28 (2005)
Herbstritt, M., Becker, B.: On Combining 01X-Logic and QBF. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2007. LNCS, vol. 4739, pp. 531–538. Springer, Heidelberg (2007)
Herbstritt, M., Becker, B., Scholl, C.: Advanced SAT-Techniques for Bounded Model Checking of Blackbox Designs. In: Microprocessor Test and Verification (MTV), pp. 37–44 (2006)
Jain, A., Boppana, V., Mukherjee, R., Jain, J., Fujita, M., Hsiao, M.: Testing, Verification, and Diagnosis in the Presence of Unknowns. In: IEEE VLSI Test Symposium (VTS), pp. 263–269 (2000)
Lewis, M., Schubert, T., Becker, B.: Multithreaded SAT Solving. In: 12th Asia and South Pacific Design Automation Conference, pp. 926–931 (2007)
Lewis, M., Schubert, T., Becker, B.: QMiraXT – A Multithreaded QBF Solver. In: Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (2009)
McMillan, K.L.: Interpolation and SAT-Based Model Checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)
Nopper, T., Scholl, C.: Approximate Symbolic Model Checking for Incomplete Designs. In: Formal Methods in Computer-Aided Design, pp. 290–305 (2004)
Nopper, T., Scholl, C.: Flexible Modeling of Unknowns in Model Checking for Incomplete Designs. In: 8. GI/ITG/GMM Workshop Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (2005)
Nopper, T., Scholl, C., Becker, B.: Computation of Minimal Counterexamples by Using Black Box Techniques and Symbolic Methods. In: IEEE Int’l Conf. on Computer-Aided Design, pp. 273–280 (2007)
OpenCores, http://www.opencores.org
Pigorsch, F., Scholl, C.: Exploiting Structure in an AIG Based QBF Solver. In: Conf. on Design, Automation and Test in Europe (DATE), April 2009, pp. 1596–1601 (2009)
QBF Solver Evaluation, http://www.qbflib.org/index_eval.php
Scholl, C., Becker, B.: Checking Equivalence for Partial Implementations. In: Design Automation Conf., pp. 238–243 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Miller, C., Kupferschmid, S., Lewis, M., Becker, B. (2010). Encoding Techniques, Craig Interpolants and Bounded Model Checking for Incomplete Designs. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-14186-7_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14185-0
Online ISBN: 978-3-642-14186-7
eBook Packages: Computer ScienceComputer Science (R0)