IEEE TCAD (ATPG)
H. Fujiwara, et al., "A design of programmable logic arrays with universal tests," IEEE Trans. on Computers, 1981.
Edward McCluskey 教授にも気に入られた論文 その後、 Stanford 大でも PLA の DFT の研究が行われた
• 2 k – 1 Θ(2 k ) where Θ = asymptotically tight bound • Less area overhead
LF 2 SR and LFSR:
• 2 k(k+1)/2 – 1 Ω (2 k ) where Ω = asymptotic lower bound • Inferior to I 2 SR in terms of area overhead
テスト生成複雑度 [Fujiwara, et al, IEEE Trans. Comp, 1982]
• Strategy 1: In each step of the algorithm, determine as many signal values as possible that can be uniquely implied .
Strategy 2: Assign a fault signal D or D’ that is uniquely determined or implied by the fault in question.
ISCAS85 ベンチマークが発表されてから3年後に,順序回路用ベンチマーク
の必要性が問われた。
ITC’88@WashingtonDC で、下記のメンバーが集まった。
Franc Brglez (MCNC, Microelectronics Center of North Carolina) Vishwani Agrawal (AT&T Bell Labs)
2010 年 (64 歳 )
The Last Byte R.Aitken@IEEE_Design&Test
ITC’99 ベンチマーク ITC’99@Atlantic City, NJ
この The Last Byte の編集者は Scott Davidson で、私に、このコ ラムを書くように依頼した。
where x is a vector of choice variables, and a := (a 1 , ..., a m ) is a vector of
parameters ( パラメータ ) that may enter the objective function and constraint.
Suppose that for each vector a, the solution is unique and denoted by x(a).
◮ A maximum-value function, denoted by M (a), is defined as follows:
“Soon after Nash ’s work, game-theoretic models began to be used in economic theory and political science,. and psychologists began studying how human subjects behave in experimental [r]
with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n +1
+ .
(a) Show that if V is concave, U is quasi-concave. (b) Show that if U is quasi-concave, V is concave. 5. Question 5 (4 points)
◮ A lottery p is a function that assigns a nonnegative number to
each prize s, where P s∈S p(s) = 1 (here p(s) is the objective
probability of obtaining the prize s given the lottery p).
◮ Let α ◦ x ⊕ (1 − α) ◦ y denote the lottery in which the prize x
with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n+1
+ .
(a) Show that if V is concave, U is quasi-concave. (b) Show that if U is quasi-concave, V is concave. 5. Question 5 (4 points)
Suppose % is a preference relation on X. Then, show the followings. (a) Re‡exive: For any x 2 X, x x.
(b) Transitive 1: For any x; y; z 2 X, if x y and y z, then x z. (c) Transitive 2: For any x; y; z 2 X, if x y and y z, then x z. (d) Transitive 3:For any x; y; z 2 X, if x y and y % z, then x % z. where and are de…ned as follows:
■ If you will not attend the ARSC general meeting on December 13, 2013, please email or fax the letter of attorney to the Organizing Committee by November 30.. Return address:2[r]