Inverting Abstract Unification for Set-Sharing

1
Inverting Abstract Unification for Set-Sharing

• Xuan Li and Lunjin Lu
• Oakland University, U.S.A

2
Backward Analysis

• Forward analysis is about If I have an input,
  what is output?
• Backward analysis is about If I have output,
  what is corresponding input?
• Many applications such as program verification
  and debugger, etc.

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The motivations

• Dream Wish some variables are definitely
  independent after execution of program.
• What is the constraint on input that make dream
  make true.
• This information can be used in automatic
  parallelization of logic program and other
  analysis.

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How complexity it is

• The function is not ONE to ONE.
• So you have many inputs.
• The closure operator is exponential.
• The data space is exponential. If there are n
  variables, there are 2(2n-1) groups.

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Our Solution

• Computing set of maximal pre-conditions.
• Computing the least superset of all maximal
  pre-condition.
• Model problem as computing maximal models of a
  Boolean formula.

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How good is it

• This is a piece of theoretic work.
• It is very elegant because of we formalize it as
  a maximal models of Boolean formula.
• It is not efficient yet.

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Implementation

• Using C.
• Support both Linux and windows.
• A good basis for future research.

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Future work

• Full backward set-sharing analysis.
• Encoding using POS formula.

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Conclusion

• A piece of elegant theoretic work.
• Still need to improve.
• Consider the program in Pos domain will. improve
  efficiency.
• It would be better to use GFP and LFP
  computation.
• Published in PPDP 2005. Http//www/acm.org/portal/