Universal Algebra and Computational Complexity Lecture 3

More documents

Recommendations

Info

The Primal Algebra Problem (PRIMAL) INPUT: a finite algebra A. QUESTION: Is A primal? Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 13 / 31
The Primal Algebra Problem (PRIMAL) INPUT: a finite algebra A. QUESTION: Is A primal? The obvious algorithm is actually a reduction to CLO. For a finite set A, let g A be your favorite binary Sheffer operation on A. Define f : PRIMAL inp → CLO inp by f : A ↦→ (A, g A ). Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 13 / 31
Page 1 and 2: Universal Algebra and Computational
Page 3 and 4: Summary of Lecture 2 Recall from Tu
Page 5 and 6: Encoding finite algebras: size matt
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: Clone Membership Problem (CLO) INPU
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 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 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

Create successful ePaper yourself

Delete template?

Save as template?