Optimized State Encoding for Esterel Programs

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Optimized State Encoding for Esterel Programs

• Dumitru POTOP-BUTUCARU

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Overview

• State of an Esterel program
• The optimizing property
• Applications

• Register removal
• State re-encoding using the optimizing
  information

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State of an Esterel program

• Esterel statements

• pq , pq , loop p end
• emit S, present S then p else q end
• signal S in p end
• trap T in p end , exit T
• suspend p when S end
• pause
• derived statements await S, abort p when S,
  sustain S , every S do p end

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State of an Esterel program

• Esterel program execution

• Esterel synchronous language
• Program execution sequence of synchronous
  execution instants (clock ticks)
• Execution instant instantaneous mapping

(current state, input signals)
(next instant state,output signals)
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State of an Esterel program

• Global state and state of a statement

• Program state state of the pause statements in
  the program
• State of a sub-statement state of the pause
  sub-statements of the given statement
• The state of a composed statement is the union
  of the states of its direct sub-statements

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State of an Esterel program

• Selection and selection tree

• Selected statement statement that has at least
  one active pause sub-statement
• The selection status of composed statement is
  the OR of the selection statuses of its direct
  sub-statements
• Selection tree the tree defined by the pause
  statements and the OR gates corresponding to the
  composed statements

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State of an Esterel program

• Selection nodes

• pause nodes
• exclusive selection nodes
• parallel selection nodes

pq present S then p else q end ?
p
q
pq ?
p
q
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State of an Esterel program

• Example

loop present I then pauseemit O1
else pauseemit O2 end present end loop
pause
pause
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State of an Esterel program

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel
loop
sustain
await
pause
pause
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The optimizing property

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel
loop
sustain
await
pause
pause
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The optimizing property

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel

loop
sustain
await
pause
pause
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The optimizing property

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel

loop
sustain
await
pause
pause
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The optimizing property

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel


loop
sustain
await
pause
pause
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The optimizing property

• Example

trap TERMINATE in loop pause emit O1
pause emit O2 end loop sustain
RUNNING await TERMINATE_SIGNAL exit
TERMINATE end trap
parallel



loop
sustain
await
pause
pause
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The optimizing property

• If a parallel statement branch cannot terminate
  then the selection status of the branch is equal,
  at each instant, with the selection status of the
  entire parallel statement

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The optimizing property

• Non-termination criteria

• The static analysis of the Esterel program that
  is done at compile time
• Cheap method (the information comes for free)

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The optimizing property

• Some statistics

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Applications

• Register removal

parallel
parallel status loop status sustain
status await status



loop
sustain
await
pause
pause
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Applications

• Register removal

parallel
parallel status loop status sustain
status await status



loop
sustain
await
pause
pause
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Applications

• Register removal

parallel status loop status sustain
status await status
await
parallel
sustain
loop
pause
pause
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Applications

• Register removal

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Applications

• State re-encoding

• Exclusive selection nodes become switches that
  choose the selected son

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Applications

• State re-encoding

• The selection tree encoding is given by the
  encoding of all the

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Applications

• State re-encoding

• The selection tree encoding is given by the
  encoding of all the sub-trees

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Applications

• State re-encoding

• The selection tree encoding is given by the
  encoding of all the sub-trees

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Applications

• State re-encoding

• The selection tree encoding is given by the
  encoding of all the sub-trees

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Applications

• State re-encoding