Facilitating Concurrency in Hybrid Programs D E C E M E C E M B E - - PowerPoint PPT Presentation
Facilitating Concurrency in Hybrid Programs D E C E M E C E M B E R E R 1 0 , 2 0 1 9 15-824: Logical Foundations of Cyber-Physical Systems (Fall 2019) Haithem Turki Long Pham Languages shape our thinking Shaden enfreu eude - Malicious
D E C E M E C E M B E R E R 1 0 , 2 0 1 9
15-824: Logical Foundations of Cyber-Physical Systems (Fall 2019) Haithem Turki Long Pham
Dictionary) Shaden enfreu eude
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Inte tera racti tion b betw tween C CPSs Int Interaction wi n within a n a CPS
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Image courtesy of http://lfcps.org/course/lfcps19.html Image courtesy of https://lfcps.org/lfcps/slides/09-time-slides.pdf
Communicating Sequential Processes, 1978
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Image courtesy of Microsoft Research
Consumer = order!coffee -> how-much?x -> pay!x -> get?y -> STOP Barista = order?y -> how-much!2 -> pay?x -> get!y -> STOP Consumer || Barista = order!coffee -> how-much!2 -> pay!2 -> get!coffee -> STOP
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Consumer = order!coffee -> how-much?x -> get?y -> pay!x -> STOP Barista = order?y -> how-much!2 -> pay?x -> get!y -> STOP Consumer || Barista = order!coffee -> how-much!2 -> STOP
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augmented syntax Our ur C Cont
ns
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Consumer = x:=1; pay!x; x:=0 Barista = pay?x; x:=x+1
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theorem prover
to handle necessary syntax
throughout existing KeYmaera X codebase
Author horing ng P Paral allel P Prog
ams
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[1] http://www.ls.cs.cmu.edu/KeYmaeraX/ Authoring parallel programs in KeYmaera X web interface
derived axioms needed to prove the safety of parallel programs
implemented
examples in current implementation Proof
for Paral allel P Prog
ams
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Parallel axioms suggested in KeYmaera X web interface
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Proof tree in KeYmaera X web interface Completed proof in KeYmaera X web interface
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state
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