Regular expressions to fsms\hardware and software techniquesPaul Cockshott

Extended regular grammars

• Sequence abe• Alternation a|b|E• Charset [a-z]• Zero or more x*• One or more x+

Reduced forms

• Sequence abe• Alternation a|b|E• Charset [a-z]• Zero or more x*• One or more x+

• Sequence• Alternation• -> a|b|c|d….• x+|ε• x+

- ε is the null character

Map to state machines

• Sequence abc

2

31 a

b

c

Map alternation

A|x|p

A

x

p

Map A+|b

A

A

b

FSM Implementations

PLA Hardware

State table in RAM Hardware Software

State table with class table

Software Software

Hardware and software FSMs

Hardware• Interpreting machine

code in a cpu• Interpreting network

addresses in a router chip

Software• Compilers• Software routers • Protocol analysers

PLA with latch

Input char State latch

clock

Next stateAction code

And planeOr plane

Productlines

AND plane

~a a ~b b

true and complement lines

a AND ~b

b

Or plane

p

q

P or q p

Advantage of PLA

• Very fast – uses the minimum logic• Lends itself to logic minimisation• Efficient layout on silicon• Method of choice for parsing simple

regular grammars at > cpu speeds in instruction decode units

RAM based FSM

1

Source data

+

Fsm table

First char index reg

Last char index

instruction

State sel

Current char

State line

Char col

hit

8 bits

6bits

8 bits

Add char class map

+Fsm table

First char index reg

Last char index

instruction

State sel

Current char

State line

Char col

hitChar class map

Advantages of char class map

• Reduces the size of the FSM table.• If we have n states we would otherwise

require 256n locations in table. With char class map we require c x n where c is the number of distinct character classes in the grammar.