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Synthesis, Analysis, and Verification Lecture 09a

Synthesis, Analysis, and Verification Lecture 09a. Abstract Interpretation. Lectures: Viktor Kuncak. Abstract Interpretation. Way to infer properties of e.g. computations Consider assignment: z = x+y Interpreter: Abstract interpreter:. Adding and Multiplying Intervals.

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Synthesis, Analysis, and Verification Lecture 09a

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  1. Synthesis, Analysis, and VerificationLecture 09a Abstract Interpretation Lectures: Viktor Kuncak

  2. Abstract Interpretation Way to infer properties of e.g. computations Consider assignment: z = x+y Interpreter: Abstract interpreter:

  3. Adding and Multiplying Intervals

  4. Programs as Control-Flow Graphs i = 0; while (i < 10) { if (i > 1) i = i + 3; else i = i + 2; }

  5. Suppose • program state given only by the value of i • initially, it is possible that i has any value • Task: for each point, find set S of possible states

  6. i = 0; while (i < 10) { if (i > 1) i = i + 3; else i = i + 2; }

  7. Sets are Given by Equations

  8. Sets are Given by Equations

  9. Approximation of Sets by Supersets

  10. Partially Ordered Families of Sets

  11. Does every element in this order have least upper bound? Dually, does it have greatest lower bound?

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