Chapter 7: Time Complexity
For Your Enjoyment
Chapter 7.2, The Class P
Key Ideas
- All reasonable deterministic computational models are polynomially
equivalent.
- In this section, polynomial differences in algorithm implementations
are ignored.
- Definition: P is the class of languages that are decidable in
polynomial time on a deterministic single-tape Turing Machine.
In other words, P = ∪k TIME(nk).
Examples of P Problems
- PATH = {<G, s, t> | G is a directed graph that has a
directed path from s to t.}. A sample algorithm appears on page 288.
- RELPRIME = {<x, y> | x and y are relatively prime}
A sample algorithm appears on page 289.
- ACFG = {<G, w> | G is a context-free grammar that
generates string w}. A sample algorithm appears on page 291.
Active Learning
Show the dynamic programming table that might result from
testing whether the following CFG generates she programs
the robot with a friend.
- S → NP VP
- VP → VP PP | V NP | programs
- PP → P NP
- NP → DET N | he | she
- DET → a | the
- N → robot | friend
- V → programs
- P → with
Test Your Comprehension
- Problem 7.3(a).
- Problem 7.4.
- Problem 7.6.