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Recursive Learning

Recursive Learning. Madhurima Maddela. Decision Tree. Traditionally used to branch and bound in the search space to generate test vectors Inefficient for hard-to-detect and redundant faults Solution! Recursive learning.

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Recursive Learning

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  1. Recursive Learning Madhurima Maddela

  2. Decision Tree • Traditionally used to branch and bound in the search space to generate test vectors • Inefficient for hard-to-detect and redundant faults • Solution! Recursive learning H. Fujiwara, T. Shimono, "On the Acceleration of Test Generation Algorithms", 13th Intl. Symp. on Fault TolerantComp., pp. 98-105, 1983.

  3. The concept • Decision tree looks for one successful solution • Recursive learning looks for necessary conditions to purge the non-solution area • Generates all the necessary assignments for a given condition, very effective around indirect implications. • Doesn’t retrace the same path twice, backtracks can be completely avoided • Can be called recursively, hence accounts for completeness. W. Kunz, “HANNIBAL: An Efficient Tool for Logic verification Based on Recursive Learning,” ICCAD, pp. 538-543, 1993. W. Kunz and D. K. Pradhan, “Recursive Learning Technique and Applications to CAD,” US Patent Application No. 08/263721

  4. Fault Propagation using Recursive Learning W. Kunz and P. Menon, “Multilevel Logic Optimization by Implication Analysis,” Proc. Int. Conj: Computer-Aided Design (ICCAD), 1994.

  5. Boolean Satisfiability (SAT) • SAT widely used for Electronic Design Automation (EDA) • Design formulation mapped using Conjunctive Normal Form (CNF) • Can employ extensively validated algorithms J. M. Silva and L. G. e Silva, “Solvingsatisfiability in combinational circuits with backtrack search and recursive learning”, XII Symposium on Integrated Circuits and Systems Design, pp,. 192-195, 2000.

  6. Recursive learning on CNF formulae J. M. Silva and L. G. e Silva, “Solving satisfiability in combinational circuits”, IEEE Design and Test of computers, pp. 16-21, 2003.

  7. Performance • Both perform the same for circuits with no backtracks (like c1355, c5315) • Recursive learning: • No aborted faults • Computation is faster • Occasionally, recursion depth runs high W. Kunz, D. K. Pradhan, "Recursive Learning: A Precise Implication Procedure and its Application to Test Generation in Digital Circuits", IEEE Trans. on Computer-Aided Design of integrated circuits and systems, vol. 13, no. 9, 1994.

  8. Summary • Can be used in combinational as well as sequential circuits • Works for different logic alphabets • Identifies indirect implications • Limiting factor - recursion depth, rmax • Not necessary in circuits with easy-to-detect solutions

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