r e l a t i o n a l r e a s o n i n g f o r m a r k o v c
play

R e l a t i o n a l R e a s o n i n g f o r M - PowerPoint PPT Presentation

Dec 16, 2023 •679 likes •1.29k views

R e l a t i o n a l R e a s o n i n g f o r M a r k o v C h a i n s i n a P r o b a b i l i s t i c G u a r d e d L a mb d a C a l c u l u s Alejandro Aguirre, Gilles Barthe, Lars

  1. R e l a t i o n a l R e a s o n i n g f o r M a r k o v C h a i n s i n a P r o b a b i l i s t i c G u a r d e d L a mb d a C a l c u l u s Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi and Deepak Garg Imdea Software, Aarhus University, University at Buffalo SUNY, MPI-SWS

  2. o n e - t i me p a d 1 0 1 1 0 1 0 1 message 1 1 0 1 0 0 1 1 key (uniformly sampled) 0 1 1 0 0 1 1 0 ciphertext K e y p r o p e r t y : p e r f e c t s e c r e c y

  3. r e l a t i o n a l p r o p e r t i e s ● t w o e x e c u t i o n s o f t h e s a me o r d i f f e r e n t p r o g r a ms two executions ● o n e c o u l d c o mp u t e b o t h a n d c o mp a r e t h e m ● i s t h e r e a b e t t e r w a y t o r e a s o n ?

  4. r e l a t i o n a l l o g i c

  5. r e l a t i o n a l l o g i c ICFP’17

  6. r e l a t i o n a l l o g i c ICFP’17

  7. r e l a t i o n a l l o g i c ICFP’17 T wo terms

  8. r e l a t i o n a l l o g i c ICFP’17 related by a property T wo terms

  9. r e l a t i o n a l l o g i c ICFP’17 related by a property T wo terms

  10. r e l a t i o n a l l o g i c How to express this exactly?

  11. r e mi n d e r : p r o b a b i l i t y ( d i s c r e t e ) d i s t r i b u t i o n ma r g i n a l s f o r y x

  12. c o u p l i n g s 1 0 1 ● l e t & i s a c o u p l i n g ● l e t U s e f u l c a s e s : & i s a R - c o u p l i n g & ( D e n o t e d )

  13. e x a mp l e : c o i n fl i p ● S o me w a y s o f c o u p l i n g t w o f a i r c o i n s : H T H T H 1/2 0 H 1/4 1/4 equality product T 0 1/2 T 1/4 1/4 H T H T H 0 1/2 H p ½ - p inequality general T 1/2 0 T ½ - p p

  14. f u n d a me n t a l l e mma I f i s a n R - c o u p l i n g o f a n d , I d e a : T o p r o v e a r e l a t i o n a l p r o p e r t y a b o u t d i s t r i b u t i o n s , w e “ s y n c r a n d o mn e s s ” t o b u i l d t h e a p p r o p r i a t e c o u p l i n g I n p a r t i c u l a r : ● ● ( s t o c h a s t i c d o mi n a n c e )

  15. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0

  16. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1

  17. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0

  18. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0

  19. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0

  20. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 T h e r e f o r e ,

  21. o n e - t i me p a d r e v i s i t e d 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 T h e r e f o r e , O n e c a n a l s o s h o w ,

  22. ( d i s c r e t e t i me ) ma r k o v c h a i n s ● d i s c r e t e s e t o f s t a t e s ● p r o b a b i l i s t i c t r a n s i t i o n f u n c t i o n S2 1/2 S1 1 1 1/2 S3

  23. r e l a t i o n a l p r o p e r t i e s r e l a t e t w o M a r k o v c h a i n s o r t w o r u n s o f t h e s a me o n e ½ ⅓ ½ ½ ⅓ ⅓ ½ ⅔ ½ ⅔ ½ ⅔ 0 1 2 1 2 0 . . . . . . w h i c h o n e i s f a s t e r ?

  24. e x a mp l e : s t o c h a s t i c d o mi n a n c e ½ ⅓ ½ ⅓ ½ ⅓ ½ ⅔ ½ ⅔ ½ ⅔ 1 2 1 2 0 0 . . . . . . 1/2 n n+1 1/2 m m+1

  25. e x a mp l e : s t o c h a s t i c d o mi n a n c e ½ ⅓ ½ ⅓ ½ ⅓ ½ ⅔ ½ ⅔ ½ ⅔ 1 2 1 2 0 0 . . . . . . 1/2 1/6 n n n n+1 1/2 1/6 m m m+1 m+1

  26. e x a mp l e : s t o c h a s t i c d o mi n a n c e ½ ⅓ ½ ⅓ ½ ⅓ ½ ⅔ ½ ⅔ ½ ⅔ 1 2 1 2 0 0 . . . . . . 1/2 1/6 1/3 n n n n n n+1 1/2 1/6 1/3 m m m m m+1 m+1

  27. e x a mp l e : s t o c h a s t i c d o mi n a n c e ½ ⅓ ½ ⅓ ½ ⅓ ½ ⅔ ½ ⅔ ½ ⅔ 1 2 1 2 0 0 . . . . . . 1/2 1/6 1/3 n n n n n n+1 1/2 1/6 1/3 m m m m m+1 m+1

  28. s o f a r ● P r o b a b i l i t i e s & M a r k o v c h a i n s a r e a u s e f u l mo d e l i n g t o o l ● S o me i n t e r e s t i n g p r o p e r t i e s a r e r e l a t i o n a l ● T h e s e c a n b e s t u d i e d w i t h c o u p l i n g s

  29. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s

  30. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s

  31. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s

  32. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s

  33. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s . . .

  34. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s . . . P r o b l e m : 1 ) N o t e x p r e s s i v e e n o u g h !

  35. r e p r e s e n t i n g M a r k o v C h a i n s ● i n fi n i t e s e q u e n c e ( s t r e a m ) o f d i s t r i b u t i o n s . . . P r o b l e m : 1 ) N o t e x p r e s s i v e e n o u g h ! 2 ) P r o b a b i l i s t i c d e p e n d e n c e

  36. r e p r e s e n t i n g M a r k o v C h a i n s ● a s d i s t r i b u t i o n s o v e r s t r e a ms . . . 0 1 2 1 2 1 0 . . . 0 -1 0 1 0 -1 -2 . . . -2 -3 -2 -3 -4 0 -1 . . .

  37. r e p r e s e n t i n g M a r k o v C h a i n s ● a s d i s t r i b u t i o n s o v e r s t r e a ms . . . 0 1 2 1 2 1 0 . . . 0 -1 0 1 0 -1 -2 . . . -2 -3 -2 -3 -4 0 -1 . . .

  38. r e p r e s e n t i n g M a r k o v C h a i n s ● a s d i s t r i b u t i o n s o v e r s t r e a ms . . . 0 1 2 1 2 1 0 . . . 0 -1 0 1 0 -1 -2 . . . -2 -3 -2 -3 -4 0 -1 . . . P r o b l e m : N o t d i s c r e t e !

  39. t h e p r o b l e m w i t h s t r e a m d e fi n i t i o n s ● A s t r e a m i s p r o d u c t i v e i f i t o u t p u t s e v e r y fi n i t e p r e fi x i n fi n i t e t i me F o r i n s t a n c e , ● E x a mp l e o f n o n - p r o d u c t i v e s t r e a m:

  40. g u a r d e d l a mb d a c a l c u l u s ● T e r ms : ● T y p e s : An element A stream now “later” [1] Clouston, R., Bizjak, A., Grathwohl, H.B., Birkedal, L.: The guarded lambda-calculus: Programming and reasoning with guarded recursion for coinductive types. ( LMCS ‘16 )

  41. s t r e a ms i n g l c time 0 0 0 1 time 1 time 2 2 0 1 . . .

  42. s t r e a ms i n g l c time 0 0 0 1 time 1 time 2 2 0 1 . . . All prefxes are discrete!

  43. p r o b a b i l i s t i c g l c ● T e r ms : ● T y p e s :

  44. s t r e a m d i s t r i b u t i o n s i n g l c time 0 0 1 2 time 1 0 1 1 0 0 2 time 2 0 1 2 0 2 1 . . .

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Lecture 10: Cryptography creditSagnik Credit: https://xkcd.com/177/ 1/20 Basic Setup ELM Elm

Lecture 10: Cryptography creditSagnik Credit: https://xkcd.com/177/ 1/20 Basic Setup ELM Elm

Lecture 10: Cryptography creditSagnik Credit: https://xkcd.com/177/ 1/20 Basic Setup ELM Elm receiver sender Credit: https://flylib.com/books/en/1.581.1.188/1/ 2/20 Recall: XOR Recall the XOR operation: M b f x y x y x b b 0 0

750 views • 58 slides
Symmetric-Key Encryption: constructions Lecture 5 PRF , Block Cipher RECALL PRG m

Symmetric-Key Encryption: constructions Lecture 5 PRF , Block Cipher RECALL PRG m

Symmetric-Key Encryption: constructions Lecture 5 PRF , Block Cipher RECALL PRG m (stream) Enc G is a PRG if {G k (x)} x {0,1}k U n(k) and G PPT A PRG can be used to obtain a one-time SC PRG K CPA-secure SKE Stream

555 views • 10 slides
Authenticated Encryption in TLS Same modelling Poor TLS track record & verification

Authenticated Encryption in TLS Same modelling Poor TLS track record & verification

Authenticated Encryption in TLS Same modelling Poor TLS track record & verification approach - Many implementation flaws - Attacks on weak cryptography concrete security: each lossy step (MD5, SHA1, ) documented by a game and a

514 views • 27 slides
Public-Key Cryptography Public-Key Cryptography Lecture 8 Public-Key Cryptography Lecture 8

Public-Key Cryptography Public-Key Cryptography Lecture 8 Public-Key Cryptography Lecture 8

Public-Key Cryptography Public-Key Cryptography Lecture 8 Public-Key Cryptography Lecture 8 Public-Key Encryption from Trapdoor OWP Public-Key Cryptography Lecture 8 Public-Key Encryption from Trapdoor OWP CCA Security El Gamal Encryption

1.78k views • 162 slides
Great Theoretical Ideas in Computer Science Lecture 27: Cryptography What is cryptography about?

Great Theoretical Ideas in Computer Science Lecture 27: Cryptography What is cryptography about?

15-251 Great Theoretical Ideas in Computer Science Lecture 27: Cryptography What is cryptography about? Adversary Eavesdropper I will cut his throat I will cut his throat What is cryptography about? loru23n8uladjkfb!#@

1.41k views • 65 slides
Frequency Examination ABCDEFGHIJKLMNOPQRSTUVWXYZ 1 31004011301001300112000000 2

Frequency Examination ABCDEFGHIJKLMNOPQRSTUVWXYZ 1 31004011301001300112000000 2

Frequency Examination ABCDEFGHIJKLMNOPQRSTUVWXYZ 1 31004011301001300112000000 2 10022210013010000010404000 3 12000000201140004013021000 4 21102201000010431000000211 5 10500021200000500030020000 6 01110022311012100000030101 Letter

621 views • 36 slides
Unbreakable Cryptosystems ??? Almost all of the practical cryptosystems are theoretically

Unbreakable Cryptosystems ??? Almost all of the practical cryptosystems are theoretically

Unbreakable Cryptosystems ??? Almost all of the practical cryptosystems are theoretically breakable given the time are theoretically breakable given the time Security Notions and computational resources. However,

307 views • 10 slides
TrustOTP: Transforming Smartphones into Secure One-Time Password Tokens He Sun, Kun Sun, Yuewu

TrustOTP: Transforming Smartphones into Secure One-Time Password Tokens He Sun, Kun Sun, Yuewu

TrustOTP: Transforming Smartphones into Secure One-Time Password Tokens He Sun, Kun Sun, Yuewu Wang, and Jiwu Jing Presented by Fengwei Zhang Wayne State University CSC 6991 Topics in Computer Security 1 Outline IntroducLon MoLvaLon

638 views • 26 slides
OTP Kerberos Kerberos Working Group IETF, Montreal July 2006 WORKING DRAFT: 30 June 2006

OTP Kerberos Kerberos Working Group IETF, Montreal July 2006 WORKING DRAFT: 30 June 2006

OTP Kerberos Kerberos Working Group IETF, Montreal July 2006 WORKING DRAFT: 30 June 2006 Background Proposal is to define extensions to Kerberos V5 (rfc4120) to support pre-authentication using an OTP Three main aims: Allow an OTP

180 views • 14 slides
Enterprise desktop at home with FreeIPA and GNOME Alexander Bokovoy ( abokovoy@redhat.com )

Enterprise desktop at home with FreeIPA and GNOME Alexander Bokovoy ( abokovoy@redhat.com )

January 30th, 2016 FOSDEM16 Enterprise desktop at home with FreeIPA and GNOME Alexander Bokovoy ( abokovoy@redhat.com ) Enterprise desktop at home with FreeIPA and GNOME 2 Enterprise? Enterprise desktop at home with FreeIPA and GNOME 3 *

978 views • 71 slides
YURY CHEMERKIN I have 10+ years of experience in information security. Im a multi-skilled

YURY CHEMERKIN I have 10+ years of experience in information security. Im a multi-skilled

S TILL S ECURE . W E E MPOWER W HAT W E H ARDEN B ECAUSE W E C AN C ONCEAL YURY CHEMERKIN MULTI-SKILLED SECURITY EXPERT CJSC ADVANCED MONITORING YURY CHEMERKIN I have 10+ years of experience in information security. Im a multi-skilled

1.43k views • 76 slides
Federal Advocacy and Policy Updates: What's New for HCBS and Self-Direction Alison Barkoff Dan

Federal Advocacy and Policy Updates: What's New for HCBS and Self-Direction Alison Barkoff Dan

Federal Advocacy and Policy Updates: What's New for HCBS and Self-Direction Alison Barkoff Dan Berland Director of Advocacy Director of Federal Policy Center for Public Representation NASDDDS abarkoff@cpr-us.org dberland@nasddds.org

817 views • 59 slides
Building&Hacking modern iOS apps Wojciech Regua @_r3ggi wojciech.regula@securing.pl

Building&Hacking modern iOS apps Wojciech Regua @_r3ggi wojciech.regula@securing.pl

www.securing.pl Building&Hacking modern iOS apps Wojciech Regua @_r3ggi wojciech.regula@securing.pl @_r3ggi wojciech.regula@securing.pl www.securing.pl www.securing.pl WHOAMI -Senior IT Security Consultant @ SecuRing -Focused on

998 views • 67 slides
Use of NSF Supercomputers Rob Gardner, University of Chicago OSG Council, Indianapolis, October

Use of NSF Supercomputers Rob Gardner, University of Chicago OSG Council, Indianapolis, October

Use of NSF Supercomputers Rob Gardner, University of Chicago OSG Council, Indianapolis, October 3, 2017 1 Acknoweledgements !! Frank Wuerthwein Edgar Fajardo Mark Neubauer, Dave Lesny & Peter Onyisi Mats Rynge Rob Quick 2 Goal

676 views • 28 slides
Governance, Risk Management and Compliance Lect. Dr. Ana-Maria Ghiran Prof. Dr. Robert Buchmann

Governance, Risk Management and Compliance Lect. Dr. Ana-Maria Ghiran Prof. Dr. Robert Buchmann

24th International Working Conference, REFSQ 2018, Utrecht, The Netherlands, March 19-22, 2018 Security Requirements Elicitation from Engineering Governance, Risk Management and Compliance Lect. Dr. Ana-Maria Ghiran Prof. Dr. Robert Buchmann

305 views • 14 slides
Enterprise desktop: improving client side in the age of Samba AD and FreeIPA Alexander Bokovoy

Enterprise desktop: improving client side in the age of Samba AD and FreeIPA Alexander Bokovoy

Principal Software Engineer, Red Hat // Samba Team SambaXP16 Enterprise desktop: improving client side in the age of Samba AD and FreeIPA Alexander Bokovoy Enterprise desktop: improving client side in the age of Samba AD and FreeIPA 2

1.33k views • 106 slides
Classification: Public 1 Protect Y Your User Accounts Like Its 2019 Thomas Konrad, SBA

Classification: Public 1 Protect Y Your User Accounts Like Its 2019 Thomas Konrad, SBA

Classification: Public 1 Protect Y Your User Accounts Like Its 2019 Thomas Konrad, SBA Research sec4dev, Feb 27 th , 2019 SBA Research gGmbH, 2019 Classification: Public 2 $ whoami Thomas Konrad $ id uid=123(tom) gid=0(SBA Research)

733 views • 52 slides
Techniques for Efficient Secure Computation Based on Yaos Protocol Yehuda Lindell Bar-Ilan

Techniques for Efficient Secure Computation Based on Yaos Protocol Yehuda Lindell Bar-Ilan

Techniques for Efficient Secure Computation Based on Yaos Protocol Yehuda Lindell Bar-Ilan University, Israel PKC 2013 Yehuda Lindell Techniques for Efficient Secure Computation 28/2/2013 1 / 39 Secure Computation Background A set of

689 views • 39 slides
MariaDB security features and best practices Robert Bindar Software Developer @MariaDB

MariaDB security features and best practices Robert Bindar Software Developer @MariaDB

MariaDB security features and best practices Robert Bindar Software Developer @MariaDB Foundation Percona Live Austin, 28-30 May 2019 Motivation - Users Potential public shaming through data breaches Massive loss of business

606 views • 42 slides
Title Slide Math 696 Class July 19, 2002 Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7

Title Slide Math 696 Class July 19, 2002 Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7

Title Slide Math 696 Class July 19, 2002 Line 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line 7 1 0 sin( x ) =?

312 views • 3 slides
Point Line Duality Let , , be a set of points. Now

Point Line Duality Let , , be a set of points. Now

Point Line Duality Let , , be a set of points. Now define a set , , of lines as follows: Dual plane Primal plane Line: :

306 views • 4 slides
JUST THE MATHS SLIDES NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by

JUST THE MATHS SLIDES NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by

JUST THE MATHS SLIDES NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by A.J.Hobson 8.5.1 Introduction 8.5.2 The straight line passing through a given point and parallel to a given vector 8.5.3 The straight line passing

510 views • 18 slides
Lect 14a - Line Arrangements: Definitions and Zone Theorem Lect 14b - Line Arrangements:

Lect 14a - Line Arrangements: Definitions and Zone Theorem Lect 14b - Line Arrangements:

Lect 14a - Line Arrangements: Definitions and Zone Theorem Lect 14b - Line Arrangements: Definitions and Zone Theorem Lect 14c - Line Arrangements: Definitions and Zone Theorem

432 views • 5 slides
Advanced Techniques for Web-based Comics @RachelNabors .com a spectrum of storytelling a

Advanced Techniques for Web-based Comics @RachelNabors .com a spectrum of storytelling a

Advanced Techniques for Web-based Comics @RachelNabors .com a spectrum of storytelling a spectrum of storytelling madefire.com goo.gl/1o8zZu Storyboard for Ferdinand the Bull taken at the Disney Family Home Museum a spectrum of

1.02k views • 63 slides

More recommend