Universal Algebra and Computational Complexity Lecture 3

More documents

Recommendations

Info

Encoding finite algebras: size matters Let A be a finite algebra (always in a finite signature). How do we encode A for computations? And what is its size? Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 3 / 31
Encoding finite algebras: size matters Let A be a finite algebra (always in a finite signature). How do we encode A for computations? And what is its size? Assume A = {0, 1, . . . , n−1}. Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 3 / 31
Page 1 and 2: Universal Algebra and Computational
Page 3: Summary of Lecture 2 Recall from Tu
Page 7 and 8: Encoding finite algebras: size matt
Page 9 and 10: Size of an algebra Define some para
Page 11 and 12: Some decision problems involving al
Page 19 and 20: Categories of answers Suppose D is
Page 21 and 22: Categories of answers Suppose D is
Page 23 and 24: An easy problem: Subalgebra Members
Page 25 and 26: An obvious upper bound for SUB-MEM
Page 27 and 28: An obvious upper bound for SUB-MEM
Page 29 and 30: The Complexity of SUB-MEM So SUB-ME
Page 35 and 36: A variation: 1-SUB-MEM 1-SUB-MEM Th
Page 37 and 38: A variation: 1-SUB-MEM 1-SUB-MEM Th
Page 39 and 40: Some tractable problems about algeb
Page 49 and 50: Clone Membership Problem (CLO) INPU
Page 51 and 52: Clone Membership Problem (CLO) INPU
Page 53 and 54: The Primal Algebra Problem (PRIMAL)
Page 55 and 56:
PRIMAL But testing primality of alg
Page 57 and 58:
MALTSEV INPUT: a finite algebra A.
Page 59 and 60:
Similar characterizations give EXPT
Page 61 and 62:
Freese & Valeriote’s theorem For
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Freese & Valeriote’s theorem Proo
Page 69 and 70:
Open Problem 2. Are the following e
Page 71 and 72:
Open Problem 2. Are the following e
Page 73 and 74:
Surprisingly, the previous problems
Page 75 and 76:
Variety Membership Problem (VAR-MEM
Page 77 and 78:
What is the “real” complexity o
Page 79 and 80:
The Equivalence of Terms problem (E
Page 81 and 82:
Obviously INEQUIV -TERM is in NP. (
Page 83 and 84:
Obviously INEQUIV -TERM is in NP. (
Page 85 and 86:
But WAIT!!!! There’s more!!!! For
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
There are a huge number of publicat
Page 93 and 94:
There are a huge number of publicat
Page 95 and 96:
An outrageous scandal Theorem (G. H
Page 97 and 98:
Equivalence of Terms Problem (corre
Page 99 and 100:
Equivalence of Terms Problem (corre
Page 101 and 102:
Two problems for relational structu
Page 103 and 104:
Fix a finite relational structure B
Page 105 and 106:
Fix a finite relational structure B
show all

Universal Algebra and Computational Complexity Lecture 3

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?