1 / 25

Correctness in Causal Systems

Correctness in Causal Systems. Eleftherios Matsikoudis UC Berkeley. Causality (Informally). … is the constraint that an effect cannot precede its cause. Relevance. Modeling and Simulation Synchronous Programming of Reactive Systems Hardware Description. Correctness. ?. f. f.

urielle-gould
Télécharger la présentation

Correctness in Causal Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Correctness in Causal Systems Eleftherios Matsikoudis UC Berkeley

  2. Causality (Informally) … is the constraint that an effectcannot precede its cause.

  3. Relevance • Modeling and Simulation • Synchronous Programming of Reactive Systems • Hardware Description

  4. Correctness ?

  5. f f f s s s s s A C B M S A B M E Systems..

  6. f f f s s s s s C S M A B A M B E ( ) f s s s = A A M C ; ( ) f s s s = B B A C ; ( ) f s s s = M M B S E ; as Fixed-Point Equations Systems..

  7. Signals V T

  8. v s s 1 2 Prefix Order

  9. ( ) d s s s s 1 2 1 2 ; Generalized Ultrametric Distance

  10. ( ( ) ) f f µ s s s s 1 2 1 2 Causal Functions

  11. ( f h i g f 6 d i 2 ¿ v ¿ o m s d f ; , e ( ) f s = ; h i t o e r w s e . Existence of Fixed Points..?

  12. ( ( ) ) f f R ± ± ¸ s s s s 2 1 2 1 0 -Causal Functions

  13. ( ) n l f i m s n 1 ! Construction of Fixed Points

  14. ( ( ) ) f f ½ s s s s 1 2 1 2 Strictly Causal Functions

  15. Zeno

  16. ( ( ( ; ) ) ) ( ( ( ( ( ( ; ) ) ) ) ) ) f f f f f f f f f Construction of Fixed Points

  17. Beyond Strict Causality..

  18. 2 ( ( ) ) ( ) t t t + x y u = ( ( ) ) K t t y x = Algebraic Loops

  19. 2 ( ( ) ) ( ) 1 0 7 2 t t t + x y u = : ( ( ) ) K 0 2 6 8 t t y x = : Algebraic Loops

  20. ( ) 1 4 1 0 9 2 7 8 2 2 t y = : : ( ) 3 0 7 2 3 2 6 1 8 t x = : : Algebraic Loops

  21. … in Simulink

  22. … in Ptolemy II

  23. ( ( ) ( ) ) f f f ½ s s s Functions Strictly Causal on Orbits

  24. ( ( ( ; ) ) ) ( ( ( ( ( ( ; ) ) ) ) ) ) f f f f f f f f f Construction of Fixed Points

  25. Conclusion Proceed with caution..

More Related