Formal Analysis of Soft Errors using Theorem Proving

Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations and pseudo random numbers in the analysis and thus are not well suited for analyzing safety-critical applications. In this paper, we present a higher-order logic theorem proving based method for modeling and analysis of soft errors in electronic circuits. Our developed infrastructure includes formalized continuous random variable pairs, their Cumulative Distribution Function (CDF) properties and independent standard uniform and Gaussian random variables. We illustrate the usefulness of our approach by modeling and analyzing soft errors in commonly used dynamic random access memory sense amplifier circuits.

[1]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[2]  Michael J. C. Gordon,et al.  Mechanizing programming logics in higher order logic , 1989 .

[3]  Yasunari Shidama,et al.  Probability on Finite Set and Real-Valued Random Variables , 2009, Formaliz. Math..

[4]  Ramakant Khazanie.  Basic probability theory and applications , 1976 .

[5]  R. Hori,et al.  A 5 V-only 64K dynamic RAM based on high S/N design , 1980, IEEE Journal of Solid-State Circuits.

[6]  Sofiène Tahar,et al.  Formalization of Entropy Measures in HOL , 2011, ITP.

[7]  Christine Paulin-Mohring,et al.  Proofs of randomized algorithms in Coq , 2006, Sci. Comput. Program..

[8]  T. May,et al.  Alpha-particle-induced soft errors in dynamic memories , 1979, IEEE Transactions on Electron Devices.

[9]  Osman Hasan,et al.  Formal probabilistic analysis using theorem proving , 2008 .

[10]  Sofiène Tahar,et al.  Formal Reasoning about Expectation Properties for Continuous Random Variables , 2009, FM.

[11]  R. W. Keyes,et al.  Effect of randomness in the distribution of impurity ions on FET thresholds in integrated electronics , 1975 .

[12]  Feng Lin,et al.  DRAM Circuit Design: Fundamental and High-Speed Topics , 2007 .

[13]  Richard J. Boulton,et al.  Theorem Proving in Higher Order Logics , 2003, Lecture Notes in Computer Science.

[14]  Sofiène Tahar,et al.  On the Formalization of the Lebesgue Integration Theory in HOL , 2010, ITP.

[15]  John Harrison,et al.  A HOL Theory of Euclidean Space , 2005, TPHOLs.

[16]  Joe Hurd,et al.  Formal verification of probabilistic algorithms , 2003 .

[17]  S. G. Chamberlain,et al.  A compact thermal noise model for the investigation of soft error rates in MOS VLSI digital circuits , 1989 .

[18]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[19]  Johannes Hölzl,et al.  Three Chapters of Measure Theory in Isabelle/HOL , 2011, ITP.