Regular expressions to fsms

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Regular expressions to fsms

• \hardware and software techniques
• Paul Cockshott

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Extended regular grammars

• Sequence abe
• Alternation abE
• Charset a-z
• Zero or more x
• One or more x

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Reduced forms

• Sequence abe
• Alternation abE
• Charset a-z
• Zero or more x
• One or more x

• Sequence
• Alternation
• -gt abcd.
• xe
• x

- e is the null character
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Map to state machines

• Sequence abc

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a
1
c
2
b
5
Map alternation
Axp
A
p
x
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Map Ab
A
A
b
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FSM Implementations
PLA Hardware
State table in RAM Hardware Software
State table with class table Software Software
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Hardware and software FSMs

• Hardware
• Interpreting machine code in a cpu
• Interpreting network addresses in a router chip

• Software
• Compilers
• Software routers
• Protocol analysers

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PLA with latch
Input char
State latch
Next state
Action code
clock
Product lines
Or plane
And plane
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AND plane
a a b b
a AND b
b
true and complement lines
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Or plane
P or q
p
p
q
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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 gt cpu speeds in instruction decode
  units

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RAM based FSM
Source data
8 bits
1
6bits
8 bits
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Add char class map
instruction
Fsm table

State sel
State line
Last char index
Char col
First char index reg
Current char
hit
Char class map
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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.