synthesis, analysis, and verification lecture 09a
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Synthesis, Analysis, and VerificationLecture 09a
Lectures: Viktor Kuncak
Abstract Interpretation
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Abstract Interpretation
Way to infer properties of e.g. computationsConsider assignment: z = x+yInterpreter:
Abstract interpreter:
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Adding and Multiplying Intervals
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Programs as Control-Flow Graphs
i = 0;while (i < 10) { if (i > 1) i = i + 3; else i = i + 2;}
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• 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
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i = 0;while (i < 10) { if (i > 1) i = i + 3; else i = i + 2;}
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Sets are Given by Equations
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Sets are Given by Equations
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Approximation of Sets by Supersets
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Partially Ordered Families of Sets
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Does every element in this order have least upper bound?
Dually, does it have greatest lower bound?