Abstract
This paper presents a formal theory to characterize symmetry in netlists and symmetry in properties. The inherent correlation between the two types of symmetry is formalized as a theorem, which provides the soundness of our symmetry reduction method. A practical tactic is introduced to effectively integrate the symmetry reduction approach in a hybrid verification environment which combines theorem proving and symbolic trajectory evaluation. Finally, the effecitveness of the symmetry reduction method is demonstrated by case studies.
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References
Aagaard MD, Jones RB, Seger C-JH (1998) Combining theorem proving and trajectory evaluation in an industrial environment. In: DAC ’98: Proceedings of the 35th annual conference on design automation, New York, NY, USA. ACM, New York, pp 538–541
Adams S, Bjork M, Melham T, Seger C-J (2007) Automatic abstraction in symbolic trajectory evaluation. In: FMCAD ’07: Proceedings of the formal methods in computer aided design, Washington, DC, USA. IEEE Computer Society, New York, pp 127–135
Brayton R, Hachtel GD, Sangiovanni-Vincentelli A, Somenzi F, Aziz A, Cheng ST, Edwards S (1996) Vis: a system for verification and synthesis. In: CAV ’96: Proceedings of the 8th international conference on computer aided verification. Springer, Berlin, pp 428–432
Clarke EM, Enders R, Filkorn T, Jha S (1996) Exploiting symmetry in temporal logic model checking. Form Methods Syst Des 9(1–2):77–104
Darbari A (2006) Symmetry reduction for STE model checking using structured models. PhD thesis, University of Oxford
Hazelhurst S, Seger C-JH (1995) A simple theorem prover based on symbolic trajectory evaluation and bdd’s. IEEE Trans CAD Integr Circuits Syst 14(4):413–422
Hung WNN, Aziz A, McMillan K (1997) Heuristic symmetry reduction for invariant verification. In: 6th IEEE/ACM international workshop on logic synthesis, May 1997
Ip CN, Dill DL (1996) Better verification through symmetry. Form Methods Syst Des 9(1–2):41–75
Li Y (2009) Formalization of symbolic trajectory semantics. http://lcs.ios.ac.cn/~lyj238/steSymmetry.html
Manku GS, Hojati R, Brayton R (1998) Structural symmetry and model checking. In: Proc intl conf comp-aided verific, pp 159–171
McMillan KL (2000) A methodology for hardware verification using compositional model checking. Sci Comput Program 37(1–3):279–309
O’Leary J, Zhao X, Gerth R, Seger C-JH (1999) Formally verifying IEEE compliance of floating-point hardware. Intel Technol J Q1:147–190
Pandey M (1997) Formal verification of memory arrays. PhD thesis, Pittsburgh, PA, USA. Chair-Bryant, Randal E
Pandey M, Raimi R, Bryant RE, Abadir MS (1997) Formal verification of content addressable memories using symbolic trajectory evaluation. In: DAC ’97: Proceedings of the 34th annual design automation conference, New York, NY, USA. ACM, New York, pp 167–172
Paulson LC (1996) ML for the working programmer. Springer, Berlin. University of Cambridge Press, Cambridge
Seger C-JH, Bryant RE (1995) Formal verification by symbolic evaluation of partially-ordered trajectories. Form Methods Syst Des 6(2):147–189
Seger C-JH, Jones RB, O’Leary JW, Melham T, Aagaard MD, Barrett C, Syme D (2005) An industrially effective environment for formal hardware verification. IEEE Trans Comput-Aided Des Integr Circuits Syst 24(9):1381–1405
Sistla AP, Godefroid P (2004) Symmetry and reduced symmetry in model checking. ACM Trans Program Lang Syst 26(4):702–734
Technical Publications and Training, Intel Corporation (2003) Forte/FL user guide edition
Tzoref R, Grumberg O (2006) Automatic refinement and vacuity detection for symbolic trajectory evaluation. In: Ball T, Jones RB (eds) CAV. Lecture notes in computer science, vol 4144. Springer, Berlin, pp 190–204
Yang J, Seger C-JH (2003) Introduction to generalized symbolic trajectory evaluation. IEEE Trans VLSI Syst 11(3):345–353
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Li, Y., Hung, W.N.N., Song, X. et al. Exploring structural symmetry automatically in symbolic trajectory evaluation. Form Methods Syst Des 39, 117–143 (2011). https://doi.org/10.1007/s10703-011-0119-z
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DOI: https://doi.org/10.1007/s10703-011-0119-z