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What is Barrington's theorem?
What is Barrington's theorem?
- A result in computational complexity theory that states that any polynomial-size formula can be computed by a branching program of width 5 and length O(4d) where d is the depth of the formula (correct)
- A result in physics that describes the behavior of particles in a magnetic field
- A result in biology that explains the process of photosynthesis in plants.
- A result in psychology that explores the effects of social media on mental health.
What is the definition of a branching program with n variables of width k and length m?
What is the definition of a branching program with n variables of width k and length m?
- A sequence of m instructions, each of which is a tuple (i, p, q) where i is the index of variable to check (1 ≤ i ≤ n), and p and q are functions from {1, 2,…, k } to {1, 2,…, k }. (correct)
- A sequence of m instructions, each of which is a tuple (i, p, q) where i is the index of variable to check (1 ≤ i ≤ n), and p and q are functions from {1, 2,…, k } to {1, 2,…, k+1 }.
- A sequence of m instructions, each of which is a tuple (i, p, q) where i is the index of variable to check (1 ≤ i ≤ n+1), and p and q are functions from {1, 2,…, k } to {1, 2,…, k }.
- A sequence of m instructions, each of which is a tuple (i, p, q) where i is the index of variable to check (1 ≤ i ≤ n), and p and q are functions from {1, 2,…, k+1 } to {1, 2,…, k+1 }.
What is the relationship between the width and length of a branching program according to Barrington's theorem?
What is the relationship between the width and length of a branching program according to Barrington's theorem?
- The width of the branching program is fixed at 5, while the length is proportional to the depth of the formula (correct)
- The width and length of the branching program are both fixed at 5.
- The width of the branching program is proportional to the length, while the length is fixed at O(4d).
- There is no relationship between the width and length of the branching program.
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