Efficient Solution of Language Equations Using Partitioned Representations Alan Mishchenko UC Berkeley, US Robert Brayton UC Berkeley, US Roland Jiang UC Berkeley, US Tiziano Villa DIEGM, University of Udine, Italy Nina Yevtushenko Tomsk State University, Tomsk, Russia
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Efficient Solution of Language Equations Using Partitioned Representations Alan Mishchenko UC Berkeley, US Robert Brayton UC Berkeley, US Roland Jiang.
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Efficient Solution of Language Equations Using Partitioned
Representations
Alan Mishchenko UC Berkeley, USRobert Brayton UC Berkeley, USRoland Jiang UC Berkeley, USTiziano Villa DIEGM, University of Udine, ItalyNina Yevtushenko Tomsk State University, Tomsk, Russia
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Overview
• Problem formulation• Example: Traffic light controller• Partitioned representation• Solution based on partitioned representation• Experimental results• Conclusion
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Problem Formulation
FixedFixed
UnknownUnknown
ii oo
uuvv
Spec
Specification Specification S S ((i,oi,o))Fixed Fixed F F ((i,v,u,oi,v,u,o))Unknown Unknown X X ((u,vu,v))
Problem:Problem: Given Given SS and and FF, find , find the Most General Solution the Most General Solution (MGS) (MGS) XX of of
SFX
SXF
Solution:Solution:
FSMFSM
FSMFSMFSM
FSMFSM
FSMFSM
FSMFSM
FSMFSMii11
ii22
oo11
oo22
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Computing Most General FSM Solution
Input: Prefix-closed specification S(i,o) and fixed part F(i,v,u,o)
Output: Most general FSM (prefix-closed progressive) solution X
begin01 X := Complete( S )02 X := Determinize( X )03 X := Complement( X )04 X := Support( X, (i,v,u,o) )05 X := Product( Complete(F), X )06 X := Support( X, (u,v) )07 X := Determinize( X )08 X := Complete( X )09 X := Complement( X ) 10 X := PrefixClose( X )11 X := Progressive( X, u ) 12 return X
end
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Example: Traffic Light Controller
SFX I O
UV
Fixed
Unknown
F
X
Specification
S
SFX z
v
Fixed
Unknown
F
X
Specification
S
General Topology This example
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Traffic Light Controller (Fixed Part).model fixed.inputs v z.outputs Acc.mv v 2 wait go.mv z 3 red green yellow.mv CS, NS 3 Fr Fg Fy.latch NS CS.reset CSFr.table ->Acc1.table v z CS ->NSwait red Fr Frgo red Fr Fgwait green Fg Fggo green Fg Fywait yellow Fy Fygo yellow Fy Fr.end
z = {red, green, yellow}
v = {wait, go}
SFX z
v
Fixed
Unknown
F
X
SpecificationS
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Traffic Light Controller (Spec).model spec.inputs z.outputs Acc.mv z 3 red green yellow.mv CS,NS 4 S1 S2 S3 S4.table ->Acc1.latch NS CS.reset CSS1.table z CS ->NSred S1 S2red S2 S3green S3 S4yellow S4 S1.end
Name is the ISCAS benchmark namei/o/cs is the number of input/output/state variablesFcs/Xcs is the partitioning of the state variablesStates(X) is the number of states in the solutionMono is the runtime of the monolithic computation in secondsPart is the runtime of partitioned computation is in secondsRatio is improvement due to the proposed method
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Conclusions
• Introduced language solving problems• Showed a simple example• Discussed partitioned representation• Presented experimental results
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Future Work
• Developing methods for finding a particular solution contained in the most general solution
• Developing efficient sequential synthesis methods without state space traversal