Qui gardera les gardiens? (Présentation FUQAC 2012)

•

0 gostou•573 visualizações

Slides for a presentation at Fondation UQAC, February 2012 (the half-dozen words throughout the slides are in French). It is intended to be a gentle introduction to the concept of software bugs, their cost, the increasing complexity of computer programs and some methods to analyze them mathematically. I leave the viewer to guess what was the speech that accompanied each drawing. Enjoy!

Tecnologia

Qui gardera les
gardiens ?
.
par
Sylvain Halle, professeur

1 serveur

3 profs* +
3 stations 11 etudiants

1 serveur
$

56 000$ fonds 3 profs* +
3 stations de recherche (2012) 11 etudiants

Toutes les
histoires
possibles

Toutes les
histoires
du livre

Toutes les
histoires
possibles

Toutes les
Toutes les histoires
histoires du livre
plausibles

Combien d'histoires possibles ?
1 2

2 1

Combien d'histoires possibles ?
1 2 1 2 3

2 1

Combien d'histoires possibles ?
1 2 1 2 3

2 1 1 3 2

Combien d'histoires possibles ?
1 2 1 2 3

2 1 1 3 2

2 1 3

Combien d'histoires possibles ?
1 2 1 2 3

2 1 1 3 2

2 1 3

2 3 1

Combien d'histoires possibles ?
1 2 1 2 3

2 1 1 3 2

2 1 3

2 3 1

3 1 2

Combien d'histoires possibles ?
1 2 1 2 3

2 1 1 3 2

2 1 3

2 3 1

3 1 2

3 2 1

Combien d'histoires possibles ?
Histoires

1 2 3 4 5
Pages

Combien d'histoires possibles ?
Histoires

1

1 2 3 4 5
Pages

Combien d'histoires possibles ?
Histoires

2
1

1 2 3 4 5
Pages

Combien d'histoires possibles ?
Histoires

6

2
1

1 2 3 4 5
Pages

Combien d'histoires possibles ?
Histoires

6 24

2
1

1 2 3 4 5
Pages

Combien d'histoires possibles ?
Histoires

6 24 120

2
1

1 2 3 4 5
Pages

LEM
7500 lignes

Chevy Volt
10 000 000 lignes

LEM
7500 lignes

Windows 7
50 000 000 lignes

Chevy Volt
10 000 000 lignes

Windows 7
50 000 000 lignes

Chevy Volt
10 000 000 lignes

1 km/h 2 trains @ 2M$ 1 km/h
10 km

2 km/h

1 km/h 2 trains @ 2M$ 1 km/h
10 km
rails @ 20M$

2 km/h

1 km/h 2 trains @ 2M$ 1 km/h
10 km
rails @ 20M$
rgot @ 3.90$
esca
2 km/h

1 km/h 2 tr ains @ 2M$ 1 km/h
10 km
rails @ 20M$
3.__0$_
@___ 9 __
ar__ot _g
esc _ g __
___ 2 km/h 0$
2 4 000 003.9

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)
Moment de l'impact ?

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)
Moment de l'impact ?
1 x t = 10 - (1 x t)

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)
Moment de l'impact ?
1 x t = 10 - (1 x t)
2 x t = 10

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)
Moment de l'impact ?
1 x t = 10 - (1 x t)
2 x t = 10
t=5

Position train 1 = 1 x t
Position train 2 = 10 - (1 x t)
Moment de l'impact ?
1 x t = 10 - (1 x t)
2 x t = 10
t=5
Distance escargot: 2 x 5 = 10 km

Sortir baguette Jeter sort

Consulter
carte

Ranger baguette Boire potion

1 2 6
4

3
5

On ne peut se servir de la potion qu'une
seule fois au cours d'une histoir

1 2 6
4

3 Modele
5

X B UG

Specification

1 2 6
4

3
5

La baguette ne doit pas etre rangee dans
le sac pour jeter un sort

On ne peut s
e servir de la
seule fois au potion qu'un
cours d'une e
histoir

La baguette
ne doit pas e
le sac pour je tre rangee d
ter un sort ans

On ne peut s
e servir de la
seule fois au potion qu'un
cours d'une e
histoir
X

La baguette
ne doit pas e
le sac pour je tre rangee d
ter un sort ans

1 2 6
X 4

3
5
Coloriage
homomorphisme de graphe (n. m.)
Si G et H sont deux graphes dont on note les sommets V(G) et V(H)
et les arêtes E(G) et E(H), une application f: V(G) → V(H) qui envoie
les sommets de G sur ceux d H est un morphisme de graphes si:
∀(u,v) ∊ E(G), (f(u),f(v)) ∊ E(H). Plus sih plement, f est un morphisme
de graphes si l'image de e arête de G est une arête de H. S'il y a
un morphisme de G dans H, on dit classiquement que G "se projette"
dans H.

$

Ouvrir compte Retirer argent

Consulter $
solde

Fermer compte Demander pret

$

1 2 6
$
4
$

3
5

Le compte ne doit pas
etre ferme pour $

retirer de l'argent

Combinatoire
des mots
Logique
mathematique

E
E

Combinatoire
des mots
Logique
mathematique Theorie des
graphes
E
E

2

MyApplication.com
c

REC 2 2

i ? 1.

2. c
c
...

Validation de traces /
Analyse de logs

REC 2 2

i ? 1.

2. c
c
...

2

MyApplication.com
c

Runtime monitoring /
Surveillance a l'execution

COVERSTO Y

32 | New Scientist | 16 October 2010

COVERSTO Y

Verified software
My computer won’t fail me

Web-browser crashes are annoyinc but as far as software malfunctions go, the
consequence are mild. With a plane’s autopilot or the control room of a nuclear power
station, it’s another matter. As our lives become ever more saturated with computers,
how can we know they won’t fail? Currently, we systematically test all conceivable
scenarios un er which they might. A better insurance might be logic. [...]

32 | New Scientist | 16 October 2010

Mais conteúdo relacionado

Destaque

Word equations are combinatorial equalities between strings of symbols, variables and functions, which can be used to model problems in a wide range of domains. While some complexity results for the solving of specific classes of equations are known, currently there does not exist a systematic equation solver. We present in this paper a reduction of the problem of solving word equations to Boolean satisfiability, and describe the implementation of a general-purpose tool that leverages existing SAT solvers for this purpose. Our solver will prove useful in the resolution of word equations, and in the computer-based exploration of various combinatorial conjectures.

Solving Equations on Words with Morphisms and Antimorphisms

Sylvain Hallé

Artifact-centric workflows describe possible executions of a business process through constraints expressed from the point of view of the documents exchanged between principals. A sequence of manipulations is deemed valid as long as every document in the workflow follows its prescribed lifecycle at all steps of the process. So far, establishing that a given workflow complies with artifact lifecycles has mostly been done through static verification, or by assuming a centralized access to all artifacts where these constraints can be monitored and enforced. We present in this paper an alternate method of enforcing document lifecycles that requires neither static verification nor single-point access. Rather, the document itself is designed to carry fragments of its history, protected from tampering using hashing and public-key encryption. Any principal involved in the process can verify at any time that a document’s history complies with a given lifecycle. Moreover, the proposed system also enforces access permissions: not all actions are visible to all principals, and one can only modify and verify what one is allowed to observe.

Decentralized Enforcement of Artifact Lifecycles

Sylvain Hallé

Runtime monitoring de propriétés temporelles par (streaming) XML

Sylvain Hallé

Information systems in general, and business processes in particular, generate a wealth of information in the form of event traces or logs. The analysis of these logs, either offline or in real-time, can be put to numerous uses: computation of various statistics, detection of anomalous patterns or compliance violations of some form of contract. However, current solutions for Complex Event Processing (CEP) generally offer only a restricted set of predefined queries on traces, and otherwise require a user to write procedural code to compute custom queries. In this presentation, we present a formal and declarative language for the manipulation of event traces.

A formalization of complex event stream processing

Sylvain Hallé

We describe work in progress on the design and implementation of an SQL-like language for performing complex queries on event streams. This language aims at providing a simple, intuitive and fully non-procedural syntax, while still preserving backwards compatibility with traditional SQL. The syntax and informal semantics of the language are introduced; multiple examples of scenarios taken from past literature are then presented, and used to compare the expressiveness and intuitiveness of the proposed language with respect to existing Complex Event Processing engines.

BeepBeep 3: A declarative event stream query engine (EDOC 2015)

Sylvain Hallé

A runtime monitor is a tool that takes as input a model of some system, and observes in real time that the sequence of events produced by a run of that system follows the specification. While existing monitoring solutions generally use finite-state machines and temporal logic as their model language, the specification is ultimately tangled with hand-written, implementation-specific details which severely limit their range of application. We present a runtime monitoring platform that clearly separates the extraction of events in the running program from the specification and monitoring process. This separation allows one to cleanly monitor first-order properties involving arbitrarily complex native program objects, while still incurring reasonable overhead.

A Runtime Monitoring Framework for Event Streams with Non-Primitive Arguments

Sylvain Hallé

We present an algorithm for the automated verification of Linear Temporal Logic formulae on event traces using an increasingly popular cloud computing framework called MapReduce. The algorithm can process multiple, arbitrary fragments of the trace in parallel, and compute its final result through a cycle of runs of MapReduce instances. Compared to classical, single-instance solutions, a proof-of-concept implementation shows through experimental evaluation how the algorithm reduces by as much as 90% the number of operations that must be performed linearly, resulting in a commensurate speed gain.

MapReduce for Parallel Trace Validation of LTL Properties

Sylvain Hallé

This presentation is an introduction to Complex Event Processing (CEP) intended for an practicioners of Runtime Verification. It first describes typical CEP problems, popular tools and their query languages. It then presents BeepBeep 3, an event stream processor that attempts to bridge the gap between RV and CEP. Thanks to BeepBeep’s generic architecture and flexible input language, queries and properties from both fields can be efficiently processed.

When RV Meets CEP (RV 2016 Tutorial)

Sylvain Hallé

Testing Web Applications Through User Interface Constraints (CASCON 2015 Talk)

Sylvain Hallé

Comparatif sièges groupe 0+ ufc que choisir

gewitter

La Mégalopole Japonaise

milonor

Formes urbaines et architecturales

Sami Sahli

فرنساوى اولى ثانوى ترم اول

أمنية وجدى

La depollution

Hedi Aloui

2012 01 19 utilisez les differentes opportunites pour vendre en ligne

COMPETITIC

Le 6 septembre au Stade de la Méditerranée à Béziers Participez aux premières rencontres industrielles de la grande Région, Accélérez votre business ! Le 6 septembre au stade de la Méditerranée, profitez des opportunités industrielles offertes par la grande région : Intersud, ce sont des rencontres B2B dédiées aux donneurs d’ordres, sous-traitants et prestataires technologiques en Languedoc-Roussillon-Midi-Pyrénées. Grâce à une étude précise des besoins et des savoir-faire identifiés, Intersud garantit des contacts qualifiés pour le développement de nouveaux courants d’affaires. http://www.intersud.biz/ Inscription : http://intersud.prollision.eu/

Intersud, rencontre B2B inversée le 6 septembre 2016

8vo tema. cerebelo.

RDXCambio climatico

Comptines nombres

Trabajo final grupo 25 a

Britomateo

Destaque (20)

Solving Equations on Words with Morphisms and Antimorphisms

Decentralized Enforcement of Artifact Lifecycles

Runtime monitoring de propriétés temporelles par (streaming) XML

A formalization of complex event stream processing

BeepBeep 3: A declarative event stream query engine (EDOC 2015)

A Runtime Monitoring Framework for Event Streams with Non-Primitive Arguments

MapReduce for Parallel Trace Validation of LTL Properties

When RV Meets CEP (RV 2016 Tutorial)

Testing Web Applications Through User Interface Constraints (CASCON 2015 Talk)

Comparatif sièges groupe 0+ ufc que choisir

La Mégalopole Japonaise

Formes urbaines et architecturales

فرنساوى اولى ثانوى ترم اول

La depollution

2012 01 19 utilisez les differentes opportunites pour vendre en ligne

Intersud, rencontre B2B inversée le 6 septembre 2016

8vo tema. cerebelo.

RDXCambio climatico

Comptines nombres

Trabajo final grupo 25 a

Mais de Sylvain Hallé

Slides of a talk given at EDOC 2023, November 3rd, 2023. Abstract: Compliance checking is the operation that consists of assessing whether every execution trace of a business process satisfies a given correctness condition. The paper introduces the notion of hyperquery, which is a calculation that involves multiple traces from a log at the same time. A particular case of hyperquery is a hypercompliance condition, which is a correctness requirement that involves the whole log instead of individual process instances. A formalization of hyperqueries is presented, along with a number of elementary operations to express hyperqueries on arbitrary logs. An implementation of these concepts in an event stream processing engine allows users to concretely evaluate hyperqueries in real time.

Monitoring Business Process Compliance Across Multiple Executions with Stream...

Sylvain Hallé

Slides of a presentation given to promote the book "CyberSecurity in a DevOps Environment" (2023). Abstract: Integrating security in the development and operation of information systems is the cornerstone of SecDevOps. From an operational perspective, one of the key activities for achieving such an integration is the detection of incidents (such as intrusions), especially in an automated manner. However, one of the stumbling blocks of an automated approach to intrusion detection is the management of the large volume of information typically produced by this type of solution. Existing works on the topic have concentrated on the reduction of volume by increasing the precision of the detection approach, thus lowering the rate of false alarms. However, another, less explored possibility is to reduce the volume of evidence gathered for each alarm raised. This chapter explores the concept of intrusion detection from the angle of complex event processing. It provides a formalization of the notion of pattern matching in a sequence of events produced by an arbitrary system, by framing the task as a runtime monitoring problem. It then focuses on the topic of incident reporting, and proposes a technique to automatically extract relevant elements of a stream that explain the occurrence of an intrusion. These relevant elements generally amount to a small fraction of all the data ingested for an alarm to be triggered, and thus help reduce the volume of evidence that needs to be examined by manual means. The approach is experimentally evaluated on a proof-of-concept implementation of these principles.

A Stream-Based Approach to Intrusion Detection

Sylvain Hallé

Event logs and event streams can be found in software systems of very diverse kinds. Analyzing the wealth of information contained in these logs can serve multiple purposes. In this tutorial, the audience will learn about BeepBeep, a versatile Java library intended to make the processing of event streams (either offline or in realtime) both fun and simple. BeepBeep is the result of more than a decade of research led by a team at Laboratoire d’informatique formelle at Université du Québec à Chicoutimi (Canada). Over the past few years, BeepBeep has been involved in a variety of case studies, and provides built-in support for writing domain-specific languages. Recently, a complete textbook has been published on BeepBeep, testifying to the maturity that the system has acquired.

Event Stream Processing with BeepBeep 3

Sylvain Hallé

(Slides for a talk given in the journal-first track of the EDOC 2022 conference.) The combination of the Internet of Things and blockchain-based technologies represents a real opportunity for supply chain and logistics protagonists, who need more dynamic, trustworthy and transparent tracking systems in order to improve their efficiency and strengthen customer confidence. In parallel, hyperconnected logistics promise more efficient and sustainable goods handling and delivery. This chapter shows how the Ethereum blockchain and smart contracts can be used to implement a shareable and secured tracking system for hyperconnected logistics. A simulation using the well-known AnyLogic software tool provides insights on the monitoring of properties depicting shipment lifecycle constraints through a stream of blockchain log events processed by BeepBeep 3, an open source stream processing engine.

Smart Contracts-Enabled Simulation for Hyperconnected Logistics

Sylvain Hallé

Boolean test input generation is the process of finding sets of values for variables of a logical expression such that a given coverage criterion is achieved. This paper presents a formal framework in which evaluating an expression produces a tree structure, and where a coverage criterion is expressed as equivalence classes induced by a particular transformation over these trees. It then defines many well-known coverage criteria as particular cases of this framework. The paper describes an algorithm to generate test suites by a reduction through a graph problem; this algorithm works in the same way regardless of the criterion considered. An experimental evaluation of this technique shows that it produces test suites that are in many cases smaller than existing tools.

Test Suite Generation for Boolean Conditions with Equivalence Class Partitioning

Sylvain Hallé

Synthia is a versatile, modular and extensible Java-based data structure generation library. It is centered on the notion of "pickers", which are objects producing values of a given type on demand. Pickers are stateful and can be given as input to other pickers; this chaining principle can generate objects whose structure follows a complex pattern. The paper describes the core principles and key features of the library, including test input shrinking, provenance tracking, and object mutation.

Synthia: a Generic and Flexible Data Structure Generator (Long Version)

Sylvain Hallé

The paper presents a theoretical foundation for test sequence generation based on an input specification. The set of possible test sequences is first partitioned according to a generic "triaging" function, which can be created from a state-machine specification in various ways. The notion of coverage metric is then expressed in terms of the categories produced by this function. Many existing test generation problems, such as t-way state or transition coverage, become particular cases of this generic framework. We then present algorithms for generating sets of test sequences providing guaranteed full coverage with respect to a metric, by building and processing a special type of graph called a Cayley graph. An implementation of these concepts is then experimentally evaluated against existing techniques, and shows it provides better performance in terms of running time and test suite size.

Test Sequence Generation with Cayley Graphs (Talk @ A-MOST 2021)

Sylvain Hallé

We describe an extension of the BeepBeep stream processing library for the offline verification of arbitrary expressions of Linear Temporal Logic using bitmap manipulations. Experimental results show that, for complex LTL formulæ containing up to 20 operators, event traces can be evaluated at a throughput of millions of events per second and provide a considerable speed-up compared to the current implementation of the tool.

Efficient Offline Monitoring of LTL with Bit Vectors (Talk at SAC 2021)

Sylvain Hallé

A Generic Explainability Framework for Function Circuits

Sylvain Hallé

Responsive Web Design (RWD) is a concept that is born from the need to provide users with a positive and intuitive experience, no matter what device they use. Complex Cascading Style Sheets (CSS) are used in RWD to smoothly change the appearance of a website based on the window width of the device being used. The paper presents an automated approach for testing these dynamic web applications, where a combination of dynamic crawling and back-end testing is used to automatically detect RWD bugs.

Detecting Responsive Web Design Bugs with Declarative Specifications

Sylvain Hallé

To run experiments on a computer, you probably write command-line scripts for various tasks: generate your data, save it into files, process and display them as plots or tables to include in a paper. But soon enough, your handful of “quick and dirty” files becomes a bunch of poorly documented scripts that generate and pass around all kinds of obscure temporary files. LabPal is a library that allows you to set up an environment for running experiments, collating their results and processing them.

Streamlining the Inclusion of Computer Experiments in Research Papers

Sylvain Hallé

This paper describes a plug-in extension of the BeepBeep 3 event stream processing engine. The extension allows one to write a custom grammar defining a particular specification language on event traces. A built-in interpreter can then convert expressions of the language into chains of BeepBeep processors through just a few lines of code, making it easy for users to create their own domain-specific languages.

Writing Domain-Specific Languages for BeepBeep

Sylvain Hallé

Information systems produce different types of event logs; in many situations, it may be desirable to look for trends inside these logs. We show how trends of various kinds can be computed over such logs in real time, using a generic framework called the trend distance workflow. Many common computations on event streams turn out to be special cases of this workflow, depending on how a handful of workflow parameters are defined. This process has been implemented and tested in a real-world event stream processing tool, called BeepBeep.

Real-Time Data Mining for Event Streams

Sylvain Hallé

Surfez sur le web quelques heures, et vous trouverez sûrement un site ou une application qui contient un bogue dans son interface graphique. Que ce soit un bouton qui ne fonctionne pas, un rectangle partiellement caché ou mal positionné, il semble que les problèmes d’interface soient notoirement difficiles à traquer! Des technologies intelligentes pourraient-elles aider les concepteurs et les développeurs à mieux tester leurs interfaces? Au Laboratoire d’informatique formelle de l’Université du Québec à Chicoutimi, nous le croyons. Nous avons développé Cornipickle, un logiciel permettant à un développeur d’énoncer, dans un langage simple et lisible, une foule de contraintes sur le positionnement et le contenu des éléments d’une interface web. Nous verrons comment Cornipickle peut s’intégrer à une application existante, détecter des problèmes, identifier les éléments qui sont fautifs et même suggérer des correctifs. Ceci permet donc à un développeur de gagner beaucoup de temps lors de la recherche des problèmes.

Technologies intelligentes d'aide au développement d'applications web (WAQ 2018)

Sylvain Hallé

Mining event streams with BeepBeep 3

Sylvain Hallé

LabPal: Repeatable Computer Experiments Made Easy (ACM Workshop Talk)

Sylvain Hallé

A "Do-It-Yourself" Specification Language with BeepBeep 3 (Talk @ Dagstuhl 2017)

Sylvain Hallé

Event Stream Processing with Multiple Threads

Sylvain Hallé

A Few Things We Heard About RV Tools (Position Paper)

Sylvain Hallé

La quantification du premier ordre en logique temporelle

Sylvain Hallé

Mais de Sylvain Hallé (20)

Monitoring Business Process Compliance Across Multiple Executions with Stream...

A Stream-Based Approach to Intrusion Detection

Event Stream Processing with BeepBeep 3

Smart Contracts-Enabled Simulation for Hyperconnected Logistics

Test Suite Generation for Boolean Conditions with Equivalence Class Partitioning

Synthia: a Generic and Flexible Data Structure Generator (Long Version)

Test Sequence Generation with Cayley Graphs (Talk @ A-MOST 2021)

Efficient Offline Monitoring of LTL with Bit Vectors (Talk at SAC 2021)

A Generic Explainability Framework for Function Circuits

Detecting Responsive Web Design Bugs with Declarative Specifications

Streamlining the Inclusion of Computer Experiments in Research Papers

Writing Domain-Specific Languages for BeepBeep

Real-Time Data Mining for Event Streams

Technologies intelligentes d'aide au développement d'applications web (WAQ 2018)

Mining event streams with BeepBeep 3

LabPal: Repeatable Computer Experiments Made Easy (ACM Workshop Talk)

A "Do-It-Yourself" Specification Language with BeepBeep 3 (Talk @ Dagstuhl 2017)

Event Stream Processing with Multiple Threads

A Few Things We Heard About RV Tools (Position Paper)

La quantification du premier ordre en logique temporelle

Qui gardera les gardiens? (Présentation FUQAC 2012)

1. Qui gardera les gardiens ? . par Sylvain Halle, professeur

3. 3 profs* + 11 etudiants

4. 3 profs* + 3 stations 11 etudiants

5. 1 serveur 3 profs* + 3 stations 11 etudiants

6. 1 serveur $ 56 000$ fonds 3 profs* + 3 stations de recherche (2012) 11 etudiants

10. Ariane V 1996

11. Ariane V 1996

12.

13. 6 rappels en 2010

14.

15. 400 000 rappels

16.

17. 59 500 000 000 $

18. TESTING

19.

20. 1. jlq ie 2. fjf ...

21.

22. p. 3 p. 8

23.

24. Toutes les histoires possibles

25. Toutes les histoires possibles Toutes les histoires du livre

26. Toutes les histoires possibles Toutes les Toutes les histoires histoires du livre plausibles

27. Toutes les histoires possibles Toutes les Toutes les histoires histoires du livre plausibles

28. Combien d'histoires possibles ?

29. Combien d'histoires possibles ? 1 2

30. Combien d'histoires possibles ? 1 2 2 1

31. Combien d'histoires possibles ? 1 2 1 2 3 2 1

32. Combien d'histoires possibles ? 1 2 1 2 3 2 1 1 3 2

33. Combien d'histoires possibles ? 1 2 1 2 3 2 1 1 3 2 2 1 3

34. Combien d'histoires possibles ? 1 2 1 2 3 2 1 1 3 2 2 1 3 2 3 1

35. Combien d'histoires possibles ? 1 2 1 2 3 2 1 1 3 2 2 1 3 2 3 1 3 1 2

36. Combien d'histoires possibles ? 1 2 1 2 3 2 1 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1

37. Combien d'histoires possibles ? Histoires 1 2 3 4 5 Pages

38. Combien d'histoires possibles ? Histoires 1 1 2 3 4 5 Pages

39. Combien d'histoires possibles ? Histoires 2 1 1 2 3 4 5 Pages

40. Combien d'histoires possibles ? Histoires 6 2 1 1 2 3 4 5 Pages

41. Combien d'histoires possibles ? Histoires 6 24 2 1 1 2 3 4 5 Pages

42. Combien d'histoires possibles ? Histoires 6 24 120 2 1 1 2 3 4 5 Pages

43. Combien d'histoires possibles ? Histoires 6 24 120 2 1 1 2 3 4 5 Pages

44.

45. LEM 7500 lignes

46. LEM 7500 lignes Chevy Volt 10 000 000 lignes

47. LEM 7500 lignes Windows 7 50 000 000 lignes Chevy Volt 10 000 000 lignes

48. Windows 7 50 000 000 lignes Chevy Volt 10 000 000 lignes

49. Windows 7 50 000 000 lignes

50.

51.

52.

53.

54. 10 km

55. 1 km/h 10 km 1 km/h

56. 1 km/h 10 km 1 km/h 2 km/h

57. 1 km/h 10 km 1 km/h 2 km/h

58. 1 km/h 2 trains @ 2M$ 1 km/h 10 km 2 km/h

59. 1 km/h 2 trains @ 2M$ 1 km/h 10 km rails @ 20M$ 2 km/h

60. 1 km/h 2 trains @ 2M$ 1 km/h 10 km rails @ 20M$ rgot @ 3.90$ esca 2 km/h

61. 1 km/h 2 tr ains @ 2M$ 1 km/h 10 km rails @ 20M$ 3.__0$_ @___ 9 __ ar__ot _g esc _ g __ ___ 2 km/h 0$ 2 4 000 003.9

62.

63. Position train 1 = 1 x t

64. Position train 1 = 1 x t Position train 2 = 10 - (1 x t)

65. Position train 1 = 1 x t Position train 2 = 10 - (1 x t) Moment de l'impact ?

66. Position train 1 = 1 x t Position train 2 = 10 - (1 x t) Moment de l'impact ? 1 x t = 10 - (1 x t)

67. Position train 1 = 1 x t Position train 2 = 10 - (1 x t) Moment de l'impact ? 1 x t = 10 - (1 x t) 2 x t = 10

68. Position train 1 = 1 x t Position train 2 = 10 - (1 x t) Moment de l'impact ? 1 x t = 10 - (1 x t) 2 x t = 10 t=5

69. Position train 1 = 1 x t Position train 2 = 10 - (1 x t) Moment de l'impact ? 1 x t = 10 - (1 x t) 2 x t = 10 t=5 Distance escargot: 2 x 5 = 10 km

70. Sortir baguette Jeter sort Consulter carte Ranger baguette Boire potion

71. 1 2 6 4 3 5

72. 1 2 6 4 3 5 On ne peut se servir de la potion qu'une seule fois au cours d'une histoir

73. 1 2 6 4 3 5

74. 1 2 6 4 3 5

75. 1 2 6 4 3 5

76. 1 2 6 4 3 5 X

77. 1 2 6 4 3 5 X B UG

78. 1 2 6 4 3 Modele 5 X B UG Specification

79. 1 2 6 4 3 Modele 5 X B UG Specification

80. 1 2 6 4 3 Modele 5 X B UG Specification

81. 1 2 6 4 3 Modele 5 X B UG Specification

82. 1 2 6 4 3 Modele 5 X B UG Specification

83. 1 2 6 4 3 Modele 5 X B UG Specification

84. 1 2 6 4 3 Modele 5 X B UG Specification

85. 1 2 6 4 3 5 La baguette ne doit pas etre rangee dans le sac pour jeter un sort

86. 1 2 6 4 3 5

87. 1 2 6 4 3 5

88. 1 2 6 4 3 5

89. 1 2 6 4 3 5

90. 1 2 6 4 3 5

91. 1 2 6 4 3 5

92.

93. On ne peut s e servir de la seule fois au potion qu'un cours d'une e histoir La baguette ne doit pas e le sac pour je tre rangee d ter un sort ans

94. On ne peut s e servir de la seule fois au potion qu'un cours d'une e histoir X La baguette ne doit pas e le sac pour je tre rangee d ter un sort ans

95. On ne peut s e servir de la seule fois au potion qu'un cours d'une e histoir X La baguette ne doit pas e le sac pour je tre rangee d ter un sort ans

96. On ne peut s e servir de la seule fois au potion qu'un cours d'une e histoir X La baguette ne doit pas e le sac pour je tre rangee d ter un sort ans

97. 1 2 6 X 4 3 5 Coloriage

98. 1 2 6 X 4 3 5 Coloriage homomorphisme de graphe (n. m.) Si G et H sont deux graphes dont on note les sommets V(G) et V(H) et les arêtes E(G) et E(H), une application f: V(G) → V(H) qui envoie les sommets de G sur ceux d H est un morphisme de graphes si: ∀(u,v) ∊ E(G), (f(u),f(v)) ∊ E(H). Plus sih plement, f est un morphisme de graphes si l'image de e arête de G est une arête de H. S'il y a un morphisme de G dans H, on dit classiquement que G "se projette" dans H.

99.

100. 720 histoires

101. 8 vérifications 720 histoires

102. Sortir baguette Jeter sort Consulter carte Ranger baguette Boire potion

103. $ Ouvrir compte Retirer argent Consulter $ solde Fermer compte Demander pret

104. 1 2 6 4 3 5 La baguette ne doit pas etre rangee dans le sac pour jeter un sort

105. $ 1 2 6 $ 4 $ 3 5 Le compte ne doit pas etre ferme pour $ retirer de l'argent

106. E E

107. Logique mathematique E E

108. Combinatoire des mots Logique mathematique E E

109. Combinatoire des mots Logique mathematique Theorie des graphes E E

110. b c a

111. b c a

112. b c a Nos recherches

113. b c a Nos recherches

114. b c a Nos recherches

115. b c a Nos recherches

116. MyApplication.com

117. 2 MyApplication.com c

118. 2 MyApplication.com c REC 2 2 i ? 1. 2. c c ...

119. REC 2 2 i ? 1. 2. c c ...

120. Validation de traces / Analyse de logs REC 2 2 i ? 1. 2. c c ...

121. MyApplication.com

122. MyApplication.com

123. 2 MyApplication.com c

124. 2 MyApplication.com c

125. 2 MyApplication.com c Runtime monitoring / Surveillance a l'execution

126. ( )

127. Synthese automatique de modele ( )

128. COVERSTO Y 32 | New Scientist | 16 October 2010

129. COVERSTO Y Verified software My computer won’t fail me Web-browser crashes are annoyinc but as far as software malfunctions go, the consequence are mild. With a plane’s autopilot or the control room of a nuclear power station, it’s another matter. As our lives become ever more saturated with computers, how can we know they won’t fail? Currently, we systematically test all conceivable scenarios un er which they might. A better insurance might be logic. [...] 32 | New Scientist | 16 October 2010

130. COVERSTO Y Verified software My computer won’t fail me Web-browser crashes are annoyinc but as far as software malfunctions go, the consequence are mild. With a plane’s autopilot or the control room of a nuclear power station, it’s another matter. As our lives become ever more saturated with computers, how can we know they won’t fail? Currently, we systematically test all conceivable scenarios un er which they might. A better insurance might be logic. [...] 32 | New Scientist | 16 October 2010

Qui gardera les gardiens? (Présentation FUQAC 2012)

Recomendados

Recomendados

Mais conteúdo relacionado

Destaque

Destaque (20)

Mais de Sylvain Hallé

Mais de Sylvain Hallé (20)

Qui gardera les gardiens? (Présentation FUQAC 2012)