osaka university knowledge archive : ouka...(12) r.j.lipton and r.sedgewick : "lower bounds in...

163
Title VLSI回路の面積と計算時間の複雑さに関する研究 Author(s) 和田, 幸一 Citation Issue Date Text Version ETD URL http://hdl.handle.net/11094/659 DOI rights Note Osaka University Knowledge Archive : OUKA Osaka University Knowledge Archive : OUKA https://ir.library.osaka-u.ac.jp/repo/ouka/all/ Osaka University

Upload: others

Post on 22-May-2020

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

Title VLSI回路の面積と計算時間の複雑さに関する研究

Author(s) 和田, 幸一

Citation

Issue Date

Text Version ETD

URL http://hdl.handle.net/11094/659

DOI

rights

Note

Osaka University Knowledge Archive : OUKAOsaka University Knowledge Archive : OUKA

https://ir.library.osaka-u.ac.jp/repo/ouka/all/

Osaka University

Page 2: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

VLSI回 路 の面積 と計算 時 聞 の

複 雑 さに関 す る研究

1::

Page 3: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 4: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 5: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 6: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

K.Wada, K.Hagihara and N.Tokura : "Area-Time Bounds for

VLSI Circuits," Proceedings 19th Annual Allerton Conference

on Communication, Control, and Computing,p.234

(September-October 1981).

Page 7: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

K.Wada, K.Hagihara and N.Tokura : "Area and Time

Complexities of VLSI Computations," Proceedings the 7th IBM

Symposium on Mathematical Foundations of Computer Science,

Mathematical Theory of Computations, IBM Japan,pp. 1-77 (June 1982).

K.Hagihara, K.Wada and N.Tokura : "Effects of Practical

Assumption Area Complexity in VLSI Computation,"_ to appear

in Lecture Notes in Computer Science, Springer-Verlag.

Page 8: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 9: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 10: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 11: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 12: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 13: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 14: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 15: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 16: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 17: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 18: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 19: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 20: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 21: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 22: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 23: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 24: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 25: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 26: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 27: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 28: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 29: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 30: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 31: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 32: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 33: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 34: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 35: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 36: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

S2 ( 2'-n'-

0 1 ) (2'-n'-

S2 1 ) (n • loga^ln)

0 (n•loga- 1 r. )

c2 (n • logo-ln )

0 (n • Toga-1n )

p (n• i oga-ln )

0 (n•log a-ln )

S2 (n•log(xn )

D (n•logan )

2 (n•loga-ln )

3 (n• log CL-1 n

2 (n•loga-1n )

D (n • logo-ln )

(k=0(n/log3n))

(n•logan ) (any k )

Page 37: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 38: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 39: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 40: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 41: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 42: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 43: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 44: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 45: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 46: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 47: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 48: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 49: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 50: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 51: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 52: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 53: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 54: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 55: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 56: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 57: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 58: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 59: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 60: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 61: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 62: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 63: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 64: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 65: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 66: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 67: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 68: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 69: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 70: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 71: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 72: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 73: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 74: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 75: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 76: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 77: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 78: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 79: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 80: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 81: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 82: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 83: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 84: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 85: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 86: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 87: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 88: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 89: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 90: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 91: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 92: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 93: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 94: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 95: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 96: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 97: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 98: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 99: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 100: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 101: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 102: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 103: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 104: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 105: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 106: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 107: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 108: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 109: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 110: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 111: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 112: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 113: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 114: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 115: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 116: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 117: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 118: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 119: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 120: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 121: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 122: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 123: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 124: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 125: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 126: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 127: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 128: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 129: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 130: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 131: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 132: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 133: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 134: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 135: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 136: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 137: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 138: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 139: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 140: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 141: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 142: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 143: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 144: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 145: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 146: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 147: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 148: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 149: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 150: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 151: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 152: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 153: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 154: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 155: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

(1) R.P.Brent and H.T.Kung : "The Area-Time Complexity of

Binary Multiplication," Technical Report CM"u-CS-79-136,

Department of Computer Science, Carnegie-Mellon University,

Pittsburgh, Pa. (July 1979).

(2) R.P.Brent and H.T.Kung : "The Chip Complexity of Binary

Arithmetic," Proceedings 12th Annual ACM Symposium. on Theory

of Computing, ACM, pp.190-200 (April 1980).

(3) R.P.Brent and .T.Kung : "On the Area of Binary Tree

Layouts," Information Processing Letters, Vol.11, No.1,

pp.46-48 (August 1980).

(4) B.Chazelle and L.Monier : "A Model of Computation for VLLSI

with Related Complexity Results," Technical Report

CMU-CS-81-1 n7 , Department of Computer Science

Carnegie-Mellon University, Pittsburgh, Pa. (February 1981).

(5) I.Deegan : "Concise Cellular Array for Multiplication and

Division," Electronics Letters, Vol.7, No.23 (November

1971).

(7) K.Hagihara, K.Wada and N.Tokura : "Effects of Practical

Assumption Area Complexity in VLSI Computation," to appear

in Lecture Notes in Computer Science, Springer-Verlag.

Page 156: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

(8) R.B.Johnson Jr. "The Complexity of a VLSI Adder,"

Information Processing Letters, Vol.11, No.2, pp.92-93

(October 1980).

(9) _D.E.Knuth : The Art of Computer Programming Vol. 3:

------Sorting and Searching, Addison-Wesley , Reading,

---- Massachusetts (1973) .

(10) H.T.Kung : "Let's Design Algorithms for VLSI Systems,"

Technical Report CMU-79--151, Department of Computer

Science,:Carnegie-Mellon University Pittsburgh, Pa . (January

1979).

(11) R.J.Lipton and R.E.Tarjan "Applications of a Planar

Separator Theorem," SIAM Journal on Computing, Vol.9, No.3,

pp.615-627 (August 1980).

(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI,"

Proceedings 13th Annual ACM Symposium on Theory of

Computing, ACM, pp.300-307 (May 1981).

(13) C.A.Mead and L.A.Conway : Introduction to VLSI Systems,

Addison-Wesley, Menlo Park(1980).

(14)_K.Menger : "Zur Allgemeinen Kurventheorie," Fundamental

_ Mathematics, Vol.10, pp.96-115 (1927).

.(15) D.E.Muller and F.P.Preparata\': "Bounds to Complexities of

Network for Sorting and for Switching," JACM, Vol.22, No.2,

----- pp .195-201 (April 1975). __

-(16) F.P.Preparata and J.E.Vuillemin "Area-Time Optimal VLSI

Networks Based on the Cube-Connected-Cycles," INRIA Rapports

de Recherche No.13 (March 1980).

(17) J.E.Savage : The Complexity of Computing,

Wiley-Interscience, New York (1976).

Page 157: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

(18) J.E.Savage : "Area-Time Tradeoffs for Matrix Multiplication

and Related Problems in VLSI Models," JCSS, Vol.22, No.2 pp.

230-242 (April 1981).

(19)_J.E.Savage : "Planar Circuit Complexity and the Performance

of VLSI Algorithms," INRIA Rapports de Recherche, No.77

(April 1981).

(20) C.D.Thompson : "A Complexity Theory for VLSI," Technical

Report CMU-80-140, Department.of Computer. Science,

Carnege-Mellon University, Pittsbur 0 i gh, Pa. (August 1980).-

(21) S.H.Unger : "Tree Realizations of Iterative Circuits," IEEE

Transactions on Computers, Vol.C-26, No.4, pp.365-383 (April

1977).

(22) J.Vuillemin : "A Combinational Limit to the Computing Power

of V.L.S.I. Circuits,"_IEEE 21st Annual Symposium on

Foundation of Computer Science, pp.294-300 (October 1980).

(26) K.Wada, K.Hagih_ara and N.Tokura.: "Area-Time Bounds for

VLSI Circuits," Proceedings 19th Annual Allerton Conference

on Communication, Control, and Computing,p.234 .

(September-October 1981).

10

Page 158: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307

(30) K.Wada, K.Hagihara and N.Tokura : "Area and Time

Complexities cf VLSI Co put ti-n59" Dr Cce~i - the 7t't- 7,01"r

Symposium on Mathematical Foundations of Computer Science ,

Mathematical Theory of Computations, IBM Japan,pp. 1-77 (June

1982).

(32) A.C.Yao : "The Entropic Limitations of VLSI Computations ,"

Proceedings 13th Annual ACM Symposium on Theory of

Computing, ACM, pp.308-311 (May 1981).

Page 159: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 160: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 161: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 162: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307
Page 163: Osaka University Knowledge Archive : OUKA...(12) R.J.Lipton and R.Sedgewick : "Lower bounds in VLSI," Proceedings 13th Annual ACM Symposium on Theory of Computing, ACM, pp.300-307