Universal Algebra and Computational Complexity Lecture 3

More documents

Recommendations

Info

Equivalence of Terms Problem (correct version) Fix a finite algebra A. The Equivalence of Circuits problem (EQUIV -CIRC(A)) INPUT: two circuits s(⃗x), t(⃗x) in the signature of A. QUESTION: is s(⃗x) ≈ t(⃗x) identically true in A? This is the correct problem. The input is presented “honestly” (computationally). It is invariant for algebras with the same clone. Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 29 / 31
Equivalence of Terms Problem (correct version) Fix a finite algebra A. The Equivalence of Circuits problem (EQUIV -CIRC(A)) INPUT: two circuits s(⃗x), t(⃗x) in the signature of A. QUESTION: is s(⃗x) ≈ t(⃗x) identically true in A? This is the correct problem. The input is presented “honestly” (computationally). It is invariant for algebras with the same clone. Open Problem 3. For which finite algebras A is EQUIV -CIRC(A) NP-complete? For which A is it in P? Ross Willard (Waterloo) Algebra and Complexity Třešť, September 2008 29 / 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 13 and 14:
Page 15 and 16:
Page 17 and 18:
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 31 and 32:
Page 33 and 34:
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 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48: 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 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: 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?