week 1 introduction to model checking
play

Week-1: Introduction to model checking B. Srivathsan Chennai - PowerPoint PPT Presentation

Sep 13, 2023 •173 likes •844 views

Week-1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 30 Module 4: Modeling concurrent systems 2 / 30 Concurrent systems Independent Shared variables Shared actions 3 / 30

  1. Week-1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 30

  2. Module 4: Modeling concurrent systems 2 / 30

  3. Concurrent systems Independent Shared variables Shared actions 3 / 30

  4. red TrLight 1 green red TrLight 2 green 4 / 30

  5. red TrLight 1 green red TrLight 2 green What is the transition system for the joint behaviour ? 4 / 30

  6. red TrLight 1 green red TrLight 2 green 5 / 30

  7. red TrLight 1 green red TrLight 2 green red , red 5 / 30

  8. red TrLight 1 green red TrLight 2 green red , red green , red red , green 5 / 30

  9. red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

  10. red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

  11. red TrLight 1 green red TrLight 2 green red , red green , red red , green green , green 5 / 30

  12. red TrLight 1 green red TrLight 2 green red , red TrLight 1 ||| TrLight 2 green , red red , green green , green 5 / 30

  13. red TrLight 1 green red TrLight 2 green red , red TrLight 1 ||| TrLight 2 green , red red , green ||| : Interleaving operator green , green 5 / 30

  14. q 1 l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 6 / 30

  15. α q 1 β l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : y=7 l 1 : x=0 α β q 2 : y=5 l 2 : x=1 TS 1 TS 2 ( initially x=0 ) ( initially y=7 ) 6 / 30

  16. α q 1 β l 1 y := y-2 x := x+1 ... ... y:= y-2 x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : y=7 l 1 : x=0 x=0 , y=7 β α α β x=1 , y=7 x=0 , y=5 α β x=1 , y=5 q 2 : y=5 l 2 : x=1 TS 1 TS 1 ||| TS 2 TS 2 ( initially x=0 ) ( initially y=7 ) 6 / 30

  17. a a q 1 q 2 ||| l 1 l 3 b a b l 2 7 / 30

  18. a a q 1 q 2 ||| l 1 l 3 b a b l 2 l 1 , q 1 l 2 , q 1 l 3 , q 1 l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

  19. a a q 1 q 2 ||| l 1 l 3 b a b l 2 a l 1 , q 1 l 2 , q 1 l 3 , q 1 a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

  20. a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

  21. a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

  22. a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a a l 1 , q 2 l 2 , q 2 l 3 , q 2 7 / 30

  23. a a q 1 q 2 ||| l 1 l 3 b a b l 2 a b l 1 , q 1 l 2 , q 1 l 3 , q 1 a a a a b b b b l 1 , q 2 l 2 , q 2 l 3 , q 2 a a 7 / 30

  24. Multiple systems TS 1 ||| TS 2 ||| ... ||| TS n 8 / 30

  25. Multiple systems TS 1 ||| TS 2 ||| ... ||| TS n Exercise: Try out an example of interleaving three systems 8 / 30

  26. Concurrent systems Independent Shared variables Interleaving TS 1 ||| TS 2 ||| ... ||| TS n Shared actions 9 / 30

  27. q 1 x:= 2 · x l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 10 / 30

  28. α q 1 x:= 2 · x β l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : x=3 l 1 : x=3 α β q 2 : x=4 l 2 : x=6 TS 1 TS 2 ( initially x=3 ) ( initially x=3 ) 10 / 30

  29. α q 1 x:= 2 · x β l 1 x:= x+1 ... ... x := 2 · x x:= x+1 q 2 l 2 PG 1 PG 2 q 1 : x=3 l 1 : x=3 x=3 , x=3 β α α β x=6 , x=3 x=3 , x=4 α β q 2 : x=4 l 2 : x=6 x=6 , x=4 TS 1 TS 1 ||| TS 2 TS 2 ( initially x=3 ) ( initially x=3 ) 10 / 30

  30. q 1 l 1 x := 2 · x x := x+1 q 2 l 2 PG 1 PG 2 11 / 30

  31. l 1 , q 1 q 1 l 1 x:=2 · x x:=x+1 ||| x := 2 · x l 2 , q 1 l 1 , q 2 x := x+1 = q 2 l 2 x:=2 · x x:=x+1 l 2 , q 2 PG 1 PG 2 PG 1 ||| PG 2 11 / 30

  32. l 1 , q 1 α q 1 β l 1 x:=2 · x x:=x+1 ||| x := 2 · x l 2 , q 1 l 1 , q 2 x := x+1 = q 2 l 2 x:=2 · x x:=x+1 l 2 , q 2 PG 1 PG 2 PG 1 ||| PG 2 l 1 , q 1 : x=3 β α TS( PG 1 ||| PG 2 ): l 2 , q 1 : x=6 l 1 , q 2 : x=4 β α l 2 , q 2 : x=7 l 2 , q 2 : x=8 11 / 30

  33. Concurrent systems Independent Shared variables Interleaving TS( PG 1 ||| PG 2 ||| ... ||| PG n ) TS 1 ||| TS 2 ||| ... ||| TS n Shared actions 12 / 30

  34. Coming next: Another example 13 / 30

  35. while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 14 / 30

  36. while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 Is the value of x always between 0 and 200? 14 / 30

  37. while x < 200 while x>0 while x=200 x := x+1 x := x-1 x := 0 m 1 n 1 l 1 x := x+1 x < 200 x:=x-1 x > 0 x:=0 x = 200 m 2 n 2 l 2 Is the value of x always between 0 and 200? 14 / 30

  38. l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 15 / 30

  39. l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 15 / 30

  40. l 1 , m 1 , n 1 x:=x+1 x=200 x:=x-1 x>0 x:=0 x<200 l 2 , m 1 , n 1 l 1 , m 2 , n 1 l 1 , m 1 , n 2 x=200 x:=x+1 x<200 x:=x-1 x>0 x:=x-1 x>0 x=200 x:=x+1 x:=0 x<200 x:=0 l 2 , m 2 , n 1 l 2 , m 1 , n 2 l 1 , m 2 , n 2 x=200 x:=x+1 x:=x-1 x>0 x:=0 x<200 l 2 , m 2 , n 2 Is the value of x always between 0 and 200? No 15 / 30

  41. Coming next: Mutual exclusion 16 / 30

  42. ... P 1 P 2 P n S HARED R ESOURCE (variable, printer, ... ) Mutual Exclusion: No two processes can access the resource simultaneously 17 / 30

  43. Goal: Modeling the protocols used for mutual exclusion 18 / 30

  44. P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . request request critical section critical section release release . . . . *non-critical actions* *non-critical actions* . . end loop end loop 19 / 30

  45. P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . request request critical section critical section release release . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 wait 1 wait 2 crit 1 crit 2 19 / 30

  46. P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . 〈 if y>0 : y:=y-1 〉 〈 if y>0 : y:=y-1 〉 *request* *request* critical section critical section y:=y+1 y:=y+1 *release* *release* . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 wait 1 wait 2 y:= y+1 y:= y+1 y>0:y:=y-1 y>0:y:=y-1 crit 1 crit 2 19 / 30

  47. P 1 P 2 loop forever loop forever . . . . *non-critical actions* *non-critical actions* . . 〈 if y>0 : y:=y-1 〉 〈 if y>0 : y:=y-1 〉 *request* *request* critical section critical section y:=y+1 y:=y+1 *release* *release* . . . . *non-critical actions* *non-critical actions* . . end loop end loop PG 1 PG 2 noncrit 1 noncrit 2 atomic wait 1 wait 2 y:= y+1 y:= y+1 y>0:y:=y-1 y>0:y:=y-1 crit 1 crit 2 19 / 30

  48. PG 1 ||| PG 2 noncrit 1 , noncrit 2 y:=y+1 y:=y+1 wait 1 , noncrit 2 noncrit 1 , wait 2 y:=y+1 y>0: y>0: y:=y-1 y:=y-1 crit 1 , noncrit 2 wait 1 , wait 2 noncrit 1 , crit 2 y>0: crit 1 , wait 2 wait 1 , crit 2 y:=y-1 y:=y+1 y:=y+1 crit 1 , crit 2 20 / 30

  49. TS( PG 1 ||| PG 2 ) n 1 , n 2 , y=1 w 1 , n 2 , y=1 n 1 , w 2 , y=1 c 1 , n 2 , y=0 w 1 , w 2 , y=1 n 1 , c 2 , y=0 c 1 , w 2 , y=0 w 1 , c 2 , y=0 21 / 30

  50. TS( PG 1 ||| PG 2 ) n 1 , n 2 , y=1 w 1 , n 2 , y=1 n 1 , w 2 , y=1 c 1 , n 2 , y=0 w 1 , w 2 , y=1 n 1 , c 2 , y=0 c 1 , w 2 , y=0 w 1 , c 2 , y=0 Both processes cannot be in critical section simultaneously 21 / 30

  51. Concurrent systems Independent Shared variables Interleaving TS( PG 1 ||| PG 2 ||| ... ||| PG n ) TS 1 ||| TS 2 ||| ... ||| TS n Mutual Exclusion Shared actions 22 / 30

  52. Coming next: Book-keeping system in a supermarket 23 / 30

  53. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 24 / 30

  54. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 000 24 / 30

  55. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 24 / 30

  56. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 check_price 010 24 / 30

  57. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 scan 100 000 001 prt_cmd check_price 010 24 / 30

  58. Bar-Code Reader (BCR) Booking Program (BP) Printer (P) 0 0 0 scan print check_price print_cmd check_price print_cmd 1 1 1 101 print check_price scan prt_cmd print print scan scan 100 000 001 110 111 011 scan prt_cmd print check_price 010 24 / 30

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

Week 1- Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course

Week 1- Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course

Week 1- Introduction to model checking B. Srivathsan Chennai Mathematical Institute NPTEL-course July - November 2015 1 / 14 Course overview 2 / 14 What are we interested in? 3 / 14 What are we interested in? Software Controllers Code that

219 views • 21 slides
Hoare Logic and Model Checking Model Checking Lecture 7: Introduction and background Dominic

Hoare Logic and Model Checking Model Checking Lecture 7: Introduction and background Dominic

Hoare Logic and Model Checking Model Checking Lecture 7: Introduction and background Dominic Mulligan Based on previous slides by Alan Mycroft and Mike Gordon Programming, Logic, and Semantics Group, University of Cambridge Academic year

972 views • 41 slides
Statistical Statistical Statistical Model Statistical Model Model Checking Model Checking

Statistical Statistical Statistical Model Statistical Model Model Checking Model Checking

Statistical Statistical Statistical Model Statistical Model Model Checking Model Checking Checking Checking for Timed Automata Timed Automata Coll C l C ll b llabora orators: t ors: Peter Bulychev, Alexandre David Axel Legay, Marius

725 views • 59 slides
Hoare Logic and Model Checking Model Checking Lecture 11: Model checking for Computation Tree

Hoare Logic and Model Checking Model Checking Lecture 11: Model checking for Computation Tree

Hoare Logic and Model Checking Model Checking Lecture 11: Model checking for Computation Tree Logic Dominic Mulligan Based on previous slides by Alan Mycroft and Mike Gordon Programming, Logic, and Semantics Group University of Cambridge

402 views • 25 slides
Introduction to Model Checking Radu Mateescu Inria Univ. Grenoble Alpes LIG What is model

Introduction to Model Checking Radu Mateescu Inria Univ. Grenoble Alpes LIG What is model

Introduction to Model Checking Radu Mateescu Inria Univ. Grenoble Alpes LIG What is model checking? Model checking is the method by which a desired behavioral property of a reactive system is verified over a given system (the model )

606 views • 32 slides
Automated Reasoning LTL Model Checking Alan Bundy Automated Reasoning LTL Model Checking

Automated Reasoning LTL Model Checking Alan Bundy Automated Reasoning LTL Model Checking

Automated Reasoning LTL Model Checking Alan Bundy Automated Reasoning LTL Model Checking Lecture 9, page 1 Introduction So far we have looked at theorem proving Powerful, especially where good sets of rewrite rules or decision procedures

639 views • 26 slides
Model Checking in Systems Biology s Brim and Milan ska and David Lubo Ce Safr

Model Checking in Systems Biology s Brim and Milan ska and David Lubo Ce Safr

Model Checking in Systems Biology s Brim and Milan ska and David Lubo Ce Safr anek Masaryk University Czech Republic SFM 2013 1/150 Outline Introduction 1 LTL Model Checking 2 Parallel LTL Model Checking 3 Discrete

2.18k views • 199 slides
Bounded Model Checking bmc Revision: 1.11 1 [BiereCimattiClarkeZhu99] uses SAT for model

Bounded Model Checking bmc Revision: 1.11 1 [BiereCimattiClarkeZhu99] uses SAT for model

Bounded Model Checking bmc Revision: 1.11 1 [BiereCimattiClarkeZhu99] uses SAT for model checking historically not the first symbolic model checking approach scales better than original BDD based techniques mostly incomplete in

521 views • 28 slides
CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL model Checking algorithms

CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL model Checking algorithms

CTL Chapter 6 Part 2 Overview Review CTL Model Checking CTL model Checking algorithms for ( U ) Counter Examples and witnesses Symbolic Model Checking (Thursday) Binary Decision Trees

740 views • 40 slides
Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model

Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model

Lecture 1: Introduction to model checking B. Srivathsan Chennai Mathematical Institute Model Checking and Systems Verification January - April 2015 1 / 25 What are we interested in? 2 / 25 What are we interested in? Software Controllers Code

1.05k views • 40 slides
Hoare Logic and Model Checking Model Checking But perhaps theres a clever way of

Hoare Logic and Model Checking Model Checking But perhaps theres a clever way of

Hoare Logic and Model Checking Model Checking But perhaps theres a clever way of compiling one into the other? Both have very different models of time How do they compare? We have seen two widely used temporal logics Relative

510 views • 10 slides
Hoare Logic and Model Checking 1. You should be able to model simple systems in NuSMV, an LTL

Hoare Logic and Model Checking 1. You should be able to model simple systems in NuSMV, an LTL

Hoare Logic and Model Checking 1. You should be able to model simple systems in NuSMV, an LTL Other interesting books: Model Checking by Clarke, Grumberg, and Peled Principles of Model Checking by Baier and Katoen 3 Course

636 views • 11 slides
VTSA10 Summer School, Luxembourg, September 2010 Introduction Probabilistic model checking

VTSA10 Summer School, Luxembourg, September 2010 Introduction Probabilistic model checking

VTSA10 Summer School, Luxembourg, September 2010 Introduction Probabilistic model checking Model checking Automated formal verification for finite-state models Finite-state model System Result Model checker e.g. SMV, Spin Counter-

776 views • 58 slides
Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and Extensible Model Checking Framework a Modular and Extensible Model Checking Framework 3rd Estonian Summer School in Computer and System Science

777 views • 31 slides
Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and Extensible Model Checking Framework a Modular and Extensible Model Checking Framework 3rd Estonian Summer School in Computer and System Science

628 views • 34 slides
Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and

Software Model Checking Using Bogor Software Model Checking Using Bogor a Modular and Extensible Model Checking Framework a Modular and Extensible Model Checking Framework 3rd Estonian Summer School in Computer and System Science

301 views • 8 slides
MACRO FORCES MACRO FORCES n #Young4Ever

MACRO FORCES MACRO FORCES n #Young4Ever

MACRO FORCES MACRO FORCES n #Young4Ever

939 views • 37 slides
Zvi Griliches Lectures 2011 Pillars of Prosperity The Political Economics of Development Clusters

Zvi Griliches Lectures 2011 Pillars of Prosperity The Political Economics of Development Clusters

Zvi Griliches_LectureIII_110525.pdf Zvi Griliches Lectures 2011 Pillars of Prosperity The Political Economics of Development Clusters Torsten Persson Lecture III NES, May 25 E. Development Assistance, F. Political Reform, and G. Lessons

914 views • 53 slides
Prs Prsrt Pt

Prs Prsrt Pt

Prs Prsrt Pt s t strs tr t ssst

720 views • 57 slides
Digital Bridge Governance Principles Transparency: Stakeholders will have Utility: The governance

Digital Bridge Governance Principles Transparency: Stakeholders will have Utility: The governance

Digital Bridge Governance Principles Transparency: Stakeholders will have Utility: The governance body will prioritize visibility into the governance bodys work use of existing information technology and opportunities to provide

495 views • 24 slides
Informatics 1: Data &amp; Analysis Lecture 2: Entities and Relationships Ian Stark School of

Informatics 1: Data &amp; Analysis Lecture 2: Entities and Relationships Ian Stark School of

Informatics 1: Data &amp; Analysis Lecture 2: Entities and Relationships Ian Stark School of Informatics The University of Edinburgh Friday 18 January 2013 Semester 2 Week 1 N I V E U R S E I H T T Y O H F G R E

343 views • 17 slides
Finite Automata: Informal Finite Automata: Informal p.1/20 Computational models The

Finite Automata: Informal Finite Automata: Informal p.1/20 Computational models The

Finite Automata: Informal Finite Automata: Informal p.1/20 Computational models The theory of computation should begin with the question: what is a computer? Finite Automata: Informal p.2/20 Computational models The theory of

1.39k views • 74 slides
ESRN Networking events (seminars, conferences, workshops) UKES2015 conference: 25-27

ESRN Networking events (seminars, conferences, workshops) UKES2015 conference: 25-27

Energy Storage SUPERGEN Umbrella body for all storage activities June 2014 June 2019 ESRN Networking events (seminars, conferences, workshops) UKES2015 conference: 25-27 th November 2015 Capital for Grid-scale

279 views • 9 slides
Investor Update 1 st Quarter 2017 May 9, 2017 Disclaimer This presentation contains

Investor Update 1 st Quarter 2017 May 9, 2017 Disclaimer This presentation contains

Investor Update 1 st Quarter 2017 May 9, 2017 Disclaimer This presentation contains forward-looking information and forward-looking statements, as defined under applicable securities laws, (hereinafter collectively referred to as forward

587 views • 19 slides

More recommend