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RALF: Reliability Analysis for Logic Faults – An Exact Algorithm and its Applications

RALF: Reliability Analysis for Logic Faults – An Exact Algorithm and its Applications. Samuel Luckenbill 1 , Ju-Yueh Lee 2 , Yu Hu 3 , Rupak Majumdar 1 , and Lei He 2 1 Computer Science Dept., UCLA 2 Electrical Engineering Dept., UCLA

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RALF: Reliability Analysis for Logic Faults – An Exact Algorithm and its Applications

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  1. RALF: Reliability Analysis for Logic Faults – An Exact Algorithm and its Applications Samuel Luckenbill1, Ju-Yueh Lee2, Yu Hu3, Rupak Majumdar1, and Lei He2 1Computer Science Dept., UCLA 2Electrical Engineering Dept., UCLA 3Electrical Engineering Dept., University of Alberta, Edmonton Canada

  2. Outline • RALF Overview • Circuit Representation • Algorithms • Experimental results

  3. RALF Features • Single-gate criticality: The probability that a flipped bit at one gate will affect the output • Full-chip fault rate: The average criticality over all gates in a circuit

  4. Applications for RALF • Circuit optimization for reliability • Random pattern-resistant fault identification to enhance testability • Optimality studies of approximate algorithms

  5. RALF System • Exact symbolic algorithm • Compiles miter to d-DNNF (similar to BDD) • Computes criticality in one pass over d-DNNF Miter Circuit CNF d-DNNF Fault Rate

  6. Miter-Based Calculation Criticality of G: Fraction of assignments to primary inputs Xi for which O = 1

  7. Compiled Circuit Representation • Deterministic Decomposable Negation Normal Form (d-DNNF) • A subset of NNF which satisfies • Decomposability • Determinism

  8. Why d-DNNF? • Almost as powerful as BDD • Polytime operations include SAT, model counting, and model enumeration • Usually more concise than BDD and faster to compile • Determinism and decomposability make the criticality computation efficient • Compiler: http://reasoning.cs.ucla.edu/c2d

  9. or and and or or or or and and and and and and and and A B  B A C  D D  C Negation Normal Form

  10. Decomposability No two children of AND share a variable or and and A,B C,D or or or or and and and and and and and and A B  B A C  D D  C

  11. Determinism No two children of OR share a satisfying assignment or and and or or or or and and and and and and and and A B  B A C  D D  C

  12. Criticality Algorithm • d-DNNF is a representation of the miter • Invariant: at each node, we compute the probability that the circuit below it evaluates to 1 • Value computed at root is the criticality of the faulty node in the miter • Computation is linear in d-DNNF size

  13. Evaluating d-DNNF (e.g. 0.5 for a uniform distribution over the inputs) L Pr(L) 1 - Pr(L) L AND Pr(AND) = Pr(α) * Pr(β)(Requires Decomposability) α β OR Pr(OR) = Pr(α) + Pr(β) (Requires Determinism) α β

  14. Tractability

  15. Random-Pattern Resistant Faults Fault Logic Masking

  16. Detection of Random-Pattern Resistant Faults

  17. Fidelity of Monte Carlo Simulation

  18. Conclusion • RALF performs surprisingly well on MCNC circuits, despite being an exact algorithm • RALF uses d-DNNF, a less powerful but usually more succinct circuit representation than BDD. • For criticality and fault-rate computation, Monte Carlo simulation is good enough for most circuits

  19. Thank you

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