1 / 20

Probabilistic Testability Measures

Probabilistic Testability Measures. Student: Shih-Chieh Wu Advisor: Chun-Yao Wang 2005.12.26 Department of Computer Science National Tsing Hua University, Taiwan. Outline. Introduction Controllability Calculation with Aliasing-Free Assignments Conclusion & Future Work. Introduction.

brac
Download Presentation

Probabilistic Testability Measures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Probabilistic Testability Measures Student: Shih-Chieh Wu Advisor: Chun-Yao Wang 2005.12.26 Department of Computer Science National Tsing Hua University, Taiwan

  2. Outline • Introduction • Controllability Calculation with Aliasing-Free Assignments • Conclusion & Future Work

  3. Introduction • As circuits become larger, the testing complexity ↑ • Every testing technique needs a basis to analyze the circuits • Testability measures • Testability of a circuit is defined by controllability and observability of it

  4. Definitions • Controllability • The difficulty of setting a particular logic signal to 0 or 1 ( 0’s controllability or 1’ controllability ) • Observability • The difficulty of observing the state of a logic signal

  5. COP Controllability Calculation(1/2) • COP controllability: • a = pr(A=1), b = pr(B=1) are 1'controllability 1 - a a a a b b a 1 - (1 - a)  (1 - b) = a + b - a  b b

  6. COP Controllability Calculation(2/2) • Example: • Problem: • Signal correlation → inaccurate result 0.5 0.25 A 0.4375 (COP) 0.5000 (exact) G2 B G1 0.5 G4 0.5 0.25 0.5 G3 C

  7. COP Observability Calculation • COP observatility: obv(G1) = pr(A=1) × obv(G2) = pr(A=1) × pr(G3=0) × obv(G4) = 0.5 × (1-0.25) × 1 = 0.375 0.5 0.25 A G2 B G1 0.5 0.4375 G4 0.5 0.25 0.5 G3 C

  8. Calculate Controllability with Accuracy • Exhausted simulation • Assume pr(A=1) = pr(B=1) = 0.5 • pr ( F=1) = 0.25 + 0.25 = 0.5 F B A controllability of minterm • 0 0 • 0 1 • 0 • 1 1 0 1 0 1 (1-0.5) × 0.5 = 0.25 0.5 × 0.5 = 0.25 A F B

  9. Outline • Introduction • Controllability Calculation with Aliasing-Free Assignments • Conclusion & Future Work

  10. Aliasing-Free Assignments (I) • For any 2-input circuits • There are = 16 functions • The denominator of output probability is 5 × 3 = 15 • The numerators of output probability distribute from 0~15 (at most = 4 bits) Assume x2 = , x1 = X2 X1 prob. of minterms (numerator) • 0 0 • 0 1 • 0 • 1 1 1 = (bit 0=2’b00) 2 = (bit 1=2’b01) 4 = (bit 2=2’b10) 8 = (bit 3=2’b11)

  11. Accurate Controllability Calculation • Associate aliasing-free probability with input controllability • Ex: pr(X2=1)=0.5, pr(X1=1)=0.5, x2= , x1= bit 0=2’b0 is 1, NOT gate: pr(X1=0) = 1-pr(X1=1) = 0.5 bit 3=2’b11 is 1, AND gate: pr(X2=1) × pr(X1=1) = 0.25 bit 1=2’b01, bit 2=2’b10, bit 3=2’b11is 1, OR gate: pr(X2=0) × pr(X1=1) + pr(X2=1) × pr(X1=0) + pr(X2=1) × pr(X1=1) = 0.75

  12. Controllability of Signal Correlation (1/2) • Assume c= , b= , a= , and controllability of C , B and A is 0.5 • bit 1 (2’b001): pr(C=0) × pr(B=0) × pr(A=1) = 0.25 • bit 5 (2’b101): pr(C=1) × pr(B=0) × pr(A=1) = 0.25 • bit 6 (2’b110): pr(C=1) × pr(B=1) × pr(A=0) = 0.25 • bit 7 (2’b111): pr(C=1) × pr(B=1) × pr(A=1) = 0.25 • Controllability of gate G4 is 0.5 + A G2 B G1 G4 Order: C, B, A G3 C

  13. Controllability of Signal Correlation (2/2) • How to calculate controllability of gate G3 • The output probability of gate G3 is • bit 6 (2’b110) is 1, denominator is 110 (order: C, B, A) • Whatever the corresponding bit of A ( bit 0 of 2’b110 ) is 0 or 1, it dose not matter • pr(C=1) × pr(B=1) × pr(A=0) = 0.125 is incorrect • pr(C=1) × pr(B=1) = 0.25 is correct

  14. Aliasing-Free Assignments (II) • For any 2-input circuits • There are = 16 functions • The denominator of output probability is 5 × 3 = 15 • The numerators of output probability distribute from 0~15 (at most = 4 bits) Assume x2 = , x1 = X2 X1 prob. of minterms (numerator) • 0 0 • 0 1 • 0 • 1 1 8 = = (bit 3=2’b11) 4 = = (bit 2=2’b10) 2 = = (bit 1=2’b01) 1 = = (bit 0=2’b00)

  15. Accurate Controllability Calculation • Associate aliasing-free probability with input controllability • Ex: pr(X2=1)=0.5, pr(X1=1)=0.5, x2= , x1= bit 0=2’b00 is 1, 2’b00=2’b11 AND gate: pr(X2=1) × pr(X1=1) = 0.25

  16. Summary • For any n-input circuits • There are functions • The denominator of output probability is an× an-1 × … × a1 • The numerators of output probability distribute from 0~ (at most bits) • bit i 's binary representation correspond to the minterm order Assume x2 = , x1 = X2 X1 prob. of minterms (numerator) • 0 0 • 0 1 • 0 • 1 1 1 = (bit 0=2’b00) 2 = (bit 1=2’b01) 4 = (bit 2=2’b10) 8 = (bit 3=2’b11)

  17. Internal Tree-Structure Replacement • Internal tree-structure gates can be re-assigned after its controllability is calculated • Assume pr(A=1)=pr(B=1)=pr(C=1)=0.5 : 0.5 0.5 order A G1 0.25 : 0.5 B G2 C C(G1)=0.25 C(G2)=0.5×0.25+0.5×(1-0.25) + (1-0.5) ×0.25=0.625

  18. Outline • Introduction • Controllability Calculation with Aliasing-Free Assignments • Conclusions & Future Work

  19. Conclusions • Aliasing-free assignments can be used to calculate accurate controllability with some rules • The required input assignments is still the limitation • Internal tree-structure replacement can be used to reduce the required input assignments

  20. Future Work • Improve the controllability calculation • 24 input assignments: 0.20 s • 25 input assignments: 0.37 s • 29 input assignments: 5.87 s • 30 input assignments: 11.77 s • 31 input assignments: 32.59 s • Combine other techniques to calculate controllability with little inaccuracy under the input assignment constrain

More Related