SLIDE 1
- Schizophrenia and Reincarnation
- ;
Introducing Safe Jumps in Esterel Olivier Tardieu Schizophrenia and - - PowerPoint PPT Presentation
Introducing Safe Jumps in Esterel Olivier Tardieu Schizophrenia and - - PowerPoint PPT Presentation
Introducing Safe Jumps in Esterel Olivier Tardieu Schizophrenia and Reincarnation Schizophrenia and Reincarnation
SLIDE 2
SLIDE 3
Efficient Reincarnation?
- ;
SLIDE 4
Non-instantaneous Goto Goto
- ;
SLIDE 5
Outline
- Esterel
- Goto
– formal semantics – restrictions
- Applications
– Automata – Schizophrenia
SLIDE 6
Syntax
- nothing
- pause
- p; q
- p || q
- loop p end
- signal S in p end
- – emit S
– present S then p else q end
SLIDE 7
Logical Semantics
- Reaction:
p, E → p’, E’
- Execution:
p ⇒ p’ ⇒ • iff
- p = program
- E = inputs + outputs
- b = terminates?
- p’ = residual
- E’ = outputs
- p, I∪O → p’, O
- p’, I’∪O’ → p’’, O’
b O O’ I I’
SLIDE 8
→
false
Rules – 1/2
→
true
→
false
→
false
→ ∪
b
→
true
→
b
→ → ∪
b∧b’ b
→
b’
→
false
→
false
→
true
∈
SLIDE 9
Rules – 2/2
→
b
∪ →
b
∈ ∈ ∈ ∈ →
b
→
b
∉ ∉ ∉ ∉ →
b
→
b
∉ ∉ ∉ ∉ →
b
→
b
∈ ∈ ∈ ∈
SLIDE 10
→ → → → → ∈
- ∈
- Examples
∈
- →
→ → →
- ∈
∈
SLIDE 11
Goto?
- Syntax
– gotolabel – pauselabel (pairwise distinct labels)
- Semantics
– Collect labels reached by the reaction – Compute residual by combining:
- initial statement
- with labels
p’ ≡ < p | L >
SLIDE 12
→
false
Labeled Logical Semantics
→
true
→
false
→
false
→ ∪
b
→ !
true
→
b
→ → ∪!∪!
b∧b’ b
→
b’
→
false
→
false
→
true
∈
Labeled Logical Semantics
→ →
true
→
false
→ !
false
→ !
false
→ ∪!∪!
b
→ !
true
→ !
b
→ ∪!∪!
b∧b’
→ !
b
→ !
b’
→ !
false
→ !
false
→
true
∈ →
false
SLIDE 13
Example – Part 1
"# # $ #→ # $ #"→ ## $ %&' $ ())*'+
SLIDE 14
State Semantics
- p ⇒ p’ ⇒ p’’ ⇒ ...
– p, I∪O → p’, O – p’, I’∪O’ → p’’, O’
- p ⇒ p’ ⇒ p’’ ⇒ ...
– p, I∪O → p’, O, L and p’ ≡ < p | L > – p’, I’∪O’ → p’’, O’, L’ and p’’ ≡ < p | L’ >
I I’ O O’
- I
I’ O O’
SLIDE 15
Example – Part 2
"# # $ #→ #
,"# #- .,"# -# .,"# -# ., -# ."# #
SLIDE 16
Example – Part 3
" # # $ #→ # ,#-.# $ #"→ ## ,##-.,# #-.
SLIDE 17
State Expansion
$ ,-. $ , -. $ ,!-.,!- $ ,!-.,!∩!/0-,!∩!/0- $ ,!-.,!- $ ,!-.,!- !⊂!/0 $ ,!-.,!- !⊂!/0 $ ,!-.,!- !⊂!/0 $ ,!-.,!- !⊂!/0
SLIDE 18
Well-formedness – Part 1
'& '' $ 1 #2 1 #2 $ 1 #2 '& 3 $ 1 #2 # $ 1 #2 # $ 1 #2
SLIDE 19
Exclusive or Compatible Statements?
- 1
2 ; 3 4 || 5 6
EXCLUSIVE EXCLUSIVE COMPATIBLE
SLIDE 20
Well-formedness – Part 2
$ "*'&' 34' $ " 5*'& '34'&
- 6 77# ⇒ 77#
6 77# ⇒ 77#
SLIDE 21
Summary
- A sound semantics of goto in Esterel
- Constraints
– non-instantaneity ⇒ no (causality) cycles – well-formedness ⇒ preserve Esterel semantics
- But powerful!
SLIDE 22
Automata
- 8 #
#
- 9
#
1 2 A B
':
SLIDE 23
- Schizophrenia and Reincarnation
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SLIDE 24
To jump or not to jump?
;
- ;
SLIDE 25
Algorithms
$
6 */ 0. */0*/0
$
6 */ 0. '/0*/0 6 '/0. 6 '/ 0.'/0 6 '/0.'/0'4 6 '/0.'/0'/0)
SLIDE 26
- Example
SLIDE 27
Multiple Reincarnation – No Goto
- ;
<
- ;
<
- ;
<
- ;
<
- ;
;
2n !!!
; <
- ;
SLIDE 28
Multiple Reincarnation – Goto
- ;
<
- ;
<
- #
- ;
<
- #
- ;
<
- ;
;
n2 !!!
SLIDE 29
Conclusion
- Introduction of safe jumps in Esterel
- A preprocessor for schizophrenia