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TechnicalDoc_HFA: partially fix up math bits

Steve Beattie 2017-11-10 21:42:34 +00:00
parent 54def75679
commit db189f30c8
1 changed files with 24 additions and 13 deletions
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TechnicalDoc_HFA.md

@ -246,28 +246,41 @@ concatenations always have the same consistent form, which simplifies
the the Factoring stage. the the Factoring stage.
left normalization rules (right normalization is opposite) left normalization rules (right normalization is opposite)
```math
(\epsilon | a) \to a | \epsilon
``` ```
(E | a) -> a | E ```math
(a | b) | c -> a | (b | c) (a | b) | c \to a | (b | c)
[b] | a -> a | [b] ```
```math
[b] | a \to a | [b]
``` ```
```math
\epsilon a \to a \epsilon
``` ```
Ea -> aE ```math
(ab)c -> a(bc) (ab)c \to a(bc)
``` ```
**TODO**: add actual tree diagrams **TODO**: add actual tree diagrams
### Factoring Patterns ### Factoring Patterns
```math
a\epsilon \to a
``` ```
aE -> a ```math
(a | a) -> a (a | a) \to a
a | (a | b) -> (a | b) ```
a | (ab) -> a (E | b) -> a (b | E) ```math
(ab) | (ac) -> a(b|c) a | (a | b) \to (a | b)
```
```math
a | (ab) \to a (\epsilon | b) \to a (b | \epsilon)
```
```math
(ab) | (ac) \to a(b|c)
``` ```
To see the tree after the apparmor\_parser has done simplification do To see the tree after the apparmor\_parser has done simplification do
@ -589,7 +602,6 @@ an uncompressed dfa representation which is a table indexing the rows
by state, the columns by input character, and the cells containing by state, the columns by input character, and the cells containing
the next state and accept information. Ignoring any extended HFA the next state and accept information. Ignoring any extended HFA
information, this would be information, this would be
```math ```math
size = (sizeof(next state)) * (# of input characters) * (# of states) + sizeof(accept index) * (# of states) size = (sizeof(next state)) * (# of input characters) * (# of states) + sizeof(accept index) * (# of states)
= (2) * 256 * s + 2 * x = (2) * 256 * s + 2 * x
@ -600,7 +612,6 @@ information, this would be
Therefore AppArmor's uncompressed encoding (2 bytes for next state, Therefore AppArmor's uncompressed encoding (2 bytes for next state,
2 bytes for accept index) takes up 514bytes of memory for each 2 bytes for accept index) takes up 514bytes of memory for each
state. The compressed table size is represented by: state. The compressed table size is represented by:
```math ```math
size = ((sizeof(base index) + sizeof(default) + sizeof(accept index)) + ((sizeof(next) + sizeof(check)) * (Average transitions per state) * (Packing factor))) * (# of states) size = ((sizeof(base index) + sizeof(default) + sizeof(accept index)) + ((sizeof(next) + sizeof(check)) * (Average transitions per state) * (Packing factor))) * (# of states)
= ((4 + 2 + 2) + ((2 + 2) * Ave * Pf)) * s = ((4 + 2 + 2) + ((2 + 2) * Ave * Pf)) * s