Lecture 9
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Transcript of Lecture 9
![Page 1: Lecture 9](https://reader033.fdocuments.us/reader033/viewer/2022060122/559579531a28ab3e318b4723/html5/thumbnails/1.jpg)
MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 1
HM Logic with Recursion
Mayank Pandey
Motilal Nehru National Institute of Technology,
Allahabad, Uttar Pradesh, India
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 2
Verifying Reactive Systems
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 3
Verifying Reactive Systems
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 4
Verifying Reactive Systems
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 5
Power of HM Logic
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 6
Power of HM Logic
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 7
Power of HM Logic
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 8
Temporal Properties: Can’t be expressed
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 9
Temporal Properties: Can’t be expressed
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 10
Temporal Properties: Can’t be expressed
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 11
Solution:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 12
Solution:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 13
Solution:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 14
Solving Equations:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 15
Solving Equations:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 16
Solving Equations:
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 17
The Lattice theory
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The Lattice theory
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Supremum and Infimum
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Supremum and Infimum
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 21
Complete Lattice and monotonic functions
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 22
Complete Lattice and monotonic functions
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MAYANK PANDEY,MNNIT ALLAHABAD, INDIA 23
Tarski’s Theorem
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Tarski’s Theorem
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Computing Fixed Points
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Computing Fixed Points
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Computing Fixed Point
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HM Logic: Denotational Semantics
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The Correspondence Theorem
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Image Finite LTS
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HM Logic and Strong Bisimilarity