Acceptance Test. Mohamed Mussa, Ferhat Khendek

Size: px
Start display at page:

Download "Acceptance Test. Mohamed Mussa, Ferhat Khendek"

Transcription

1 Acceptance Optimization Mohamed Mussa, Ferhat Khendek SAM 2014

2 Outline Background Problem Statement Overall Approach Integration test cases selection Comparing test models Conclusion 2

3 Background process consists of several phases Unit ing Integration ing Acceptance ing Models Model Models Model Model Model 3

4 Background - Model Based ing Development Process Model CODE Execution Model CODE ing Process 4

5 Background -Model Based ing Different approaches for different test phases Unit, integration, acceptance Different notations/languages Different subsets of the same language Many test models are produced during different phases Redundancy generation/planning: no reusability Execution: no optimization 5

6 Background - Model Based Framework Goals Provide a systematic transition between the test phases Framework Strengthen the collaboration between the development and the testing teams Well know standards & reuse Improve the test process Enable reusability & optimization

7 Background - Model Based Framework Unit Unit test model cn Unit test model c1 Integration Integration test model int(n-1) Integration test model int1 Acceptance Optimized acceptance test model Acceptance test model 7

8 Problem Statement cases may be exercised several times across the testing phases Integration vs. Acceptance Goal: remove redundant acceptance test cases Reduce test execution time 8

9 Problem Statement Obvious solution Compare integration test cases and acceptance test cases Problem Some integration test cases may include stubs for subsequent system components Cannot be substituted to acceptance test cases Comp 1 Model 1 Comp 2 SbSys 1 Comp 3 Model 2 SbSys 2 Comp 4 Model n-1 SbSys n-1 Model n System Comp n 9

10 Overall Approach Integration test cases selection Compare integration test cases to acceptance test cases 10

11 Integration test cases selection cases of last integration round are applied on complete system Compare the behavior of test stubs of each test case to the behavior of CUTs of test cases of subsequent integration rounds No additional information beside the test models Comp 1 Model 1 Comp 2 SbSys 1 Comp 3 Model 2 SbSys 2 Comp 4 Model n-1 SbSys n-1 Model n System Comp n 11

12 Integration test cases selection stubs can be specified explicitly, or «Context» TC k SbSys k CUT k+1 m1 m2 m3 «Component» stub k m6 m5 m4 specified implicitly «Context» TC k m1 m3 SbSys k m2 CUT k+1 m4 m6 m5 12

13 Integration test cases selection Event based comparison Not instance based comparison Instances are different Not event name based but message event types: message, time, miscellaneous 13

14 Integration test cases selection Selection condition Let T k = {I k, E k, R k } be an integration test case at integration round k, T i = {I i, E i, R i } be an integration test case at integration round i, i> k T k does not use a test stub for the CUT of T i if and only if ( e, e ) e E, e E ( e e ) ( e = e ) ( e. owner. st SUT ) i k i i k k i k ( ). i k i 14

15 Integration test cases selection Comparing integration test cases Round k+1 Subsequent rounds «Context» TC k m1 m3 SbSys k m2 CUT k+1 «Context» TC m SbSys m CUT m+1 s1 s2 s4 s3 m4 m6 m5 «Context» TC n m1 SbSys n m3 CUT n+1 m6 m4 15

16 Integration test cases selection cases, which their stubs do not match with subsequent CUTs, are comparedtoacceptancetestcases 16

17 Comparing Models A lot of work has been done Compared models are evolved from the same source Two-Way vs. Three-Way Look up for differences (Add/Delete/Modify) Structure vs. Behavior Our case Models did not necessary evolve from the same source 17

18 Comparing Models Comparing MSCs or Sequence Diagrams is not straightforward Several researchers have tackled this issue But this is not difficult for test cases Finite behaviors 18

19 Comparing Models A test case T is a tuple(i, E, R), where I : a set of instances E : a set of events R (E x E): a partial order reflecting the transitive closure of the order relation between events on the same axis and the sending and reception events of the same message case inclusion T acc = {I a, E a, R a } and T int = {I i, E i, R i } T acc is included in T int iff E a E i R a R i 19

20 Comparing Models Comparing test cases Acceptance test case Integration test cases «Context» TC a m1 Sys «Context» TC m SbSys m CUT m+1 s1 s2 s4 s3 m6 «Context» TC n SbSys n CUT n+1 m1 m3 m6 m4 20

21 Conclusion We proposed an optimization approach that reduces the acceptance test suite length already done at integration phase Implemented and completed the framework What kind of systems would benefit? Requires evaluation of the gain 21

Introduction to functions

Introduction to functions Introduction to functions Comp Sci 1570 Introduction to C++ Outline 1 2 Functions A function is a reusable sequence of s designed to do a particular job. In C++, a function is a group of s that is given

More information

An Extension for MSC-2000 and its Application

An Extension for MSC-2000 and its Application 1. An Extension for MSC-2000 and its Application Tong Zheng and Ferhat Khendek Department of Electrical and Computer Engineering Concordia University 1455 de Maisonneuve W., Montreal (P.Q.) Canada H3G

More information

Correspondence between Kripke Structures and Labeled Transition Systems for Model Minimization

Correspondence between Kripke Structures and Labeled Transition Systems for Model Minimization Correspondence between Kripke Structures and Labeled Transition Systems for Model Minimization Rob Schoren Abstract This document is mainly an extension of the work of Michel Reniers and Tim Willemse,

More information

Kevin James. MTHSC 206 Section 12.5 Equations of Lines and Planes

Kevin James. MTHSC 206 Section 12.5 Equations of Lines and Planes MTHSC 206 Section 12.5 Equations of Lines and Planes Definition A line in R 3 can be described by a point and a direction vector. Given the point r 0 and the direction vector v. Any point r on the line

More information

106 CHAPTER 3. TOPOLOGY OF THE REAL LINE. 2. The set of limit points of a set S is denoted L (S)

106 CHAPTER 3. TOPOLOGY OF THE REAL LINE. 2. The set of limit points of a set S is denoted L (S) 106 CHAPTER 3. TOPOLOGY OF THE REAL LINE 3.3 Limit Points 3.3.1 Main Definitions Intuitively speaking, a limit point of a set S in a space X is a point of X which can be approximated by points of S other

More information

Introduction to Computer Programming

Introduction to Computer Programming Introduction to Computer Programming Lecture 01 Software engineering is a field of engineering, for designing and writing programs for computers or other electronic devices. A software engineer, or programmer,

More information

Notes on Integrable Functions and the Riesz Representation Theorem Math 8445, Winter 06, Professor J. Segert. f(x) = f + (x) + f (x).

Notes on Integrable Functions and the Riesz Representation Theorem Math 8445, Winter 06, Professor J. Segert. f(x) = f + (x) + f (x). References: Notes on Integrable Functions and the Riesz Representation Theorem Math 8445, Winter 06, Professor J. Segert Evans, Partial Differential Equations, Appendix 3 Reed and Simon, Functional Analysis,

More information

Formal Methods for Probabilistic Systems

Formal Methods for Probabilistic Systems Formal Methods for Probabilistic Systems Annabelle McIver Carroll Morgan Source-level program logic Meta-theorems for loops Examples Relational operational model Standard, deterministic, terminating...

More information

Mathematical Induction

Mathematical Induction Mathematical Induction MAT231 Transition to Higher Mathematics Fall 2014 MAT231 (Transition to Higher Math) Mathematical Induction Fall 2014 1 / 21 Outline 1 Mathematical Induction 2 Strong Mathematical

More information

Computational Group Theory

Computational Group Theory Computational Group Theory Soria Summer School 2009 Session 3: Coset enumeration July 2009, Hans Sterk (sterk@win.tue.nl) Where innovation starts Coset enumeration: contents 2/25 What is coset enumeration

More information

Production Inference, Nonmonotonicity and Abduction

Production Inference, Nonmonotonicity and Abduction Production Inference, Nonmonotonicity and Abduction Alexander Bochman Computer Science Department, Holon Academic Institute of Technology, Israel e-mail: bochmana@hait.ac.il Abstract We introduce a general

More information

Let us first give some intuitive idea about a state of a system and state transitions before describing finite automata.

Let us first give some intuitive idea about a state of a system and state transitions before describing finite automata. Finite Automata Automata (singular: automation) are a particularly simple, but useful, model of computation. They were initially proposed as a simple model for the behavior of neurons. The concept of a

More information

Axioms of Kleene Algebra

Axioms of Kleene Algebra Introduction to Kleene Algebra Lecture 2 CS786 Spring 2004 January 28, 2004 Axioms of Kleene Algebra In this lecture we give the formal definition of a Kleene algebra and derive some basic consequences.

More information

COMP232 - Mathematics for Computer Science

COMP232 - Mathematics for Computer Science COMP232 - Mathematics for Computer Science Tutorial 9 Ali Moallemi moa ali@encs.concordia.ca Iraj Hedayati h iraj@encs.concordia.ca Concordia University, Winter 2017 Ali Moallemi, Iraj Hedayati COMP232

More information

Computer-Aided Program Design

Computer-Aided Program Design Computer-Aided Program Design Spring 2015, Rice University Unit 3 Swarat Chaudhuri February 5, 2015 Temporal logic Propositional logic is a good language for describing properties of program states. However,

More information

What do metamodels really look like?

What do metamodels really look like? What do metamodels really look like? James R. Williams, Athanasios Zolotas, Nicholas Matragkas, Louis M. Rose, Dimitios S. Kolovos, Richard F. Paige, and Fiona A. C. Polack Department of Computer Science

More information

Model Based Testing -- FSM based testing

Model Based Testing -- FSM based testing Model Based Testing -- FSM based testing Brian Nielsen {bnielsen}@cs.aau.dk Automated Model Based Conformance Testing x>=2 Model DBLclick! click? x:=0 click? x

More information

Outline. We will now investigate the structure of this important set.

Outline. We will now investigate the structure of this important set. The Reals Outline As we have seen, the set of real numbers, R, has cardinality c. This doesn't tell us very much about the reals, since there are many sets with this cardinality and cardinality doesn't

More information

Sublinear Algorithms for Big Data

Sublinear Algorithms for Big Data Sublinear Algorithms for Big Data Qin Zhang 1-1 2-1 Part 2: Sublinear in Communication Sublinear in communication The model x 1 = 010011 x 2 = 111011 x 3 = 111111 x k = 100011 Applicaitons They want to

More information

Counting Methods. CSE 191, Class Note 05: Counting Methods Computer Sci & Eng Dept SUNY Buffalo

Counting Methods. CSE 191, Class Note 05: Counting Methods Computer Sci & Eng Dept SUNY Buffalo Counting Methods CSE 191, Class Note 05: Counting Methods Computer Sci & Eng Dept SUNY Buffalo c Xin He (University at Buffalo) CSE 191 Discrete Structures 1 / 48 Need for Counting The problem of counting

More information

SFWR ENG 2FA3: Discrete Mathematics and Logic II

SFWR ENG 2FA3: Discrete Mathematics and Logic II Mathematics and Outline Dr. Ridha Khedri 1 1 Department of Computing and Software, McMaster University Canada L8S 4L7, Hamilton, Ontario Outline of Part I 1 Main topics in the course outline Topics Outline

More information

Research Statement Christopher Hardin

Research Statement Christopher Hardin Research Statement Christopher Hardin Brief summary of research interests. I am interested in mathematical logic and theoretical computer science. Specifically, I am interested in program logics, particularly

More information

FORMALISING SITUATED LEARNING IN COMPUTER-AIDED DESIGN

FORMALISING SITUATED LEARNING IN COMPUTER-AIDED DESIGN FORMALISING SITUATED LEARNING IN COMPUTER-AIDED DESIGN JOHN.S.GERO AND GOURABMOY NATH Key Centre of Design Computing Department of Architectural and Design Science University of Sydney NS W 2006 Australia

More information

A Framework for. Security Analysis. with Team Automata

A Framework for. Security Analysis. with Team Automata A Framework for Security Analysis with Team Automata Marinella Petrocchi Istituto di Informatica e Telematica National Research Council IIT-CNR Pisa, Italy Tuesday 8 June 2004 DIMACS with Maurice ter Beek

More information

Introduction to Kleene Algebras

Introduction to Kleene Algebras Introduction to Kleene Algebras Riccardo Pucella Basic Notions Seminar December 1, 2005 Introduction to Kleene Algebras p.1 Idempotent Semirings An idempotent semiring is a structure S = (S, +,, 1, 0)

More information

Decidability and Undecidability

Decidability and Undecidability Decidability and Undecidability Major Ideas from Last Time Every TM can be converted into a string representation of itself. The encoding of M is denoted M. The universal Turing machine U TM accepts an

More information

Analysis of Bounds on Hybrid Vector Clocks

Analysis of Bounds on Hybrid Vector Clocks Analysis of Bounds on Hybrid Vector Clocks Sorrachai Yingchareonthawornchai 1, Sandeep Kulkarni 2, and Murat Demirbas 3 Michigan State University 1,2 University at Buffalo 3 (OPODIS 2015) Motivation A

More information

What happens to the value of the expression x + y every time we execute this loop? while x>0 do ( y := y+z ; x := x:= x z )

What happens to the value of the expression x + y every time we execute this loop? while x>0 do ( y := y+z ; x := x:= x z ) Starter Questions Feel free to discuss these with your neighbour: Consider two states s 1 and s 2 such that s 1, x := x + 1 s 2 If predicate P (x = y + 1) is true for s 2 then what does that tell us about

More information

Modeling and Analysis of Communicating Systems

Modeling and Analysis of Communicating Systems Modeling and Analysis of Communicating Systems Lecture 5: Sequential Processes Jeroen Keiren and Mohammad Mousavi j.j.a.keiren@vu.nl and m.r.mousavi@hh.se Halmstad University March 2015 Outline Motivation

More information

Designing and Evaluating Generic Ontologies

Designing and Evaluating Generic Ontologies Designing and Evaluating Generic Ontologies Michael Grüninger Department of Industrial Engineering University of Toronto gruninger@ie.utoronto.ca August 28, 2007 1 Introduction One of the many uses of

More information

Systems of modal logic

Systems of modal logic 499 Modal and Temporal Logic Systems of modal logic Marek Sergot Department of Computing Imperial College, London utumn 2008 Further reading: B.F. Chellas, Modal logic: an introduction. Cambridge University

More information

Tues Feb Vector spaces and subspaces. Announcements: Warm-up Exercise:

Tues Feb Vector spaces and subspaces. Announcements: Warm-up Exercise: Math 2270-004 Week 7 notes We will not necessarily finish the material from a given day's notes on that day. We may also add or subtract some material as the week progresses, but these notes represent

More information

Absence of Global Clock

Absence of Global Clock Absence of Global Clock Problem: synchronizing the activities of different part of the system (e.g. process scheduling) What about using a single shared clock? two different processes can see the clock

More information

Metasonic AG 2009: German Telekom became Investor

Metasonic AG  2009: German Telekom became Investor November 2012 WWW.METASONIC.DE Metasonic AG 2004: Founding of Metasonic AG Innovative Solutions for Business Process Management 2008: Start of International Marketing 2009: German Telekom became Investor

More information

Outline F eria AADL behavior 1/ 78

Outline F eria AADL behavior 1/ 78 Outline AADL behavior Annex Jean-Paul Bodeveix 2 Pierre Dissaux 3 Mamoun Filali 2 Pierre Gaufillet 1 François Vernadat 2 1 AIRBUS-FRANCE 2 FéRIA 3 ELLIDIS SAE AS2C Detroit Michigan April 2006 FéRIA AADL

More information

Consistent Global States of Distributed Systems: Fundamental Concepts and Mechanisms. CS 249 Project Fall 2005 Wing Wong

Consistent Global States of Distributed Systems: Fundamental Concepts and Mechanisms. CS 249 Project Fall 2005 Wing Wong Consistent Global States of Distributed Systems: Fundamental Concepts and Mechanisms CS 249 Project Fall 2005 Wing Wong Outline Introduction Asynchronous distributed systems, distributed computations,

More information

6.841/18.405J: Advanced Complexity Wednesday, April 2, Lecture Lecture 14

6.841/18.405J: Advanced Complexity Wednesday, April 2, Lecture Lecture 14 6.841/18.405J: Advanced Complexity Wednesday, April 2, 2003 Lecture Lecture 14 Instructor: Madhu Sudan In this lecture we cover IP = PSPACE Interactive proof for straightline programs. Straightline program

More information

Compilers. Lexical analysis. Yannis Smaragdakis, U. Athens (original slides by Sam

Compilers. Lexical analysis. Yannis Smaragdakis, U. Athens (original slides by Sam Compilers Lecture 3 Lexical analysis Yannis Smaragdakis, U. Athens (original slides by Sam Guyer@Tufts) Big picture Source code Front End IR Back End Machine code Errors Front end responsibilities Check

More information

S ) is wf as well. (Exercise) The main example for a wf Relation is the membership Relation = {( x, y) : x y}

S ) is wf as well. (Exercise) The main example for a wf Relation is the membership Relation = {( x, y) : x y} (October 14/2010) 1 Well-foundedness Let R be a Relation on the class X ( R X X ) We say that the structure ( X, R ) is well-founded (wf) if the following holds true: Y X { x X [ y( yrx y Y) x Y]} Y =

More information

THE UTP SUITE YOUR ALL-IN-ONE SOLUTION FOR BUILDING MODERN TEST SYSTEM SOFTWARE

THE UTP SUITE YOUR ALL-IN-ONE SOLUTION FOR BUILDING MODERN TEST SYSTEM SOFTWARE THE UTP SUITE YOUR ALL-IN-ONE SOLUTION FOR BUILDING MODERN TEST SYSTEM SOFTWARE UTP Suite THE UTP SUITE DEVELOPING A STANDARD Increasing customer requirements, shorter product cycles and higher time to

More information

Problem set #4. Due February 19, x 1 x 2 + x 3 + x 4 x 5 = 0 x 1 + x 3 + 2x 4 = 1 x 1 x 2 x 4 x 5 = 1.

Problem set #4. Due February 19, x 1 x 2 + x 3 + x 4 x 5 = 0 x 1 + x 3 + 2x 4 = 1 x 1 x 2 x 4 x 5 = 1. Problem set #4 Due February 19, 218 The letter V always denotes a vector space. Exercise 1. Find all solutions to 2x 1 x 2 + x 3 + x 4 x 5 = x 1 + x 3 + 2x 4 = 1 x 1 x 2 x 4 x 5 = 1. Solution. First we

More information

Equivalence of DFAs and NFAs

Equivalence of DFAs and NFAs CS 172: Computability and Complexity Equivalence of DFAs and NFAs It s a tie! DFA NFA Sanjit A. Seshia EECS, UC Berkeley Acknowledgments: L.von Ahn, L. Blum, M. Blum What we ll do today Prove that DFAs

More information

A CLOSURE SYSTEM FOR ELEMENTARY SITUATIONS

A CLOSURE SYSTEM FOR ELEMENTARY SITUATIONS Bulletin of the Section of Logic Volume 11:3/4 (1982), pp. 134 138 reedition 2009 [original edition, pp. 134 139] Bogus law Wolniewicz A CLOSURE SYSTEM FOR ELEMENTARY SITUATIONS 1. Preliminaries In [4]

More information

Non-Interactive ZK:The Feige-Lapidot-Shamir protocol

Non-Interactive ZK:The Feige-Lapidot-Shamir protocol Non-Interactive ZK: The Feige-Lapidot-Shamir protocol April 20, 2009 Remainders FLS protocol Definition (Interactive proof system) A pair of interactive machines (P, V ) is called an interactive proof

More information

1 Introduction. 1.1 The Problem Domain. Self-Stablization UC Davis Earl Barr. Lecture 1 Introduction Winter 2007

1 Introduction. 1.1 The Problem Domain. Self-Stablization UC Davis Earl Barr. Lecture 1 Introduction Winter 2007 Lecture 1 Introduction 1 Introduction 1.1 The Problem Domain Today, we are going to ask whether a system can recover from perturbation. Consider a children s top: If it is perfectly vertically, you can

More information

15. Polynomial rings Definition-Lemma Let R be a ring and let x be an indeterminate.

15. Polynomial rings Definition-Lemma Let R be a ring and let x be an indeterminate. 15. Polynomial rings Definition-Lemma 15.1. Let R be a ring and let x be an indeterminate. The polynomial ring R[x] is defined to be the set of all formal sums a n x n + a n 1 x n +... a 1 x + a 0 = a

More information

Math General Topology Fall 2012 Homework 11 Solutions

Math General Topology Fall 2012 Homework 11 Solutions Math 535 - General Topology Fall 2012 Homework 11 Solutions Problem 1. Let X be a topological space. a. Show that the following properties of a subset A X are equivalent. 1. The closure of A in X has empty

More information

Lecture 20: Lower Bounds for Inner Product & Indexing

Lecture 20: Lower Bounds for Inner Product & Indexing 15-859: Information Theory and Applications in TCS CMU: Spring 201 Lecture 20: Lower Bounds for Inner Product & Indexing April 9, 201 Lecturer: Venkatesan Guruswami Scribe: Albert Gu 1 Recap Last class

More information

CW-complexes. Stephen A. Mitchell. November 1997

CW-complexes. Stephen A. Mitchell. November 1997 CW-complexes Stephen A. Mitchell November 1997 A CW-complex is first of all a Hausdorff space X equipped with a collection of characteristic maps φ n α : D n X. Here n ranges over the nonnegative integers,

More information

198:538 Complexity of Computation Lecture 16 Rutgers University, Spring March 2007

198:538 Complexity of Computation Lecture 16 Rutgers University, Spring March 2007 198:538 Complexity of Computation Lecture 16 Rutgers University, Spring 2007 8 March 2007 In this lecture we discuss Shamir s theorem that PSPACE is the set of languages that have interactive proofs with

More information

3. Categories and Functors We recall the definition of a category: Definition 3.1. A category C is the data of two collections. The first collection

3. Categories and Functors We recall the definition of a category: Definition 3.1. A category C is the data of two collections. The first collection 3. Categories and Functors We recall the definition of a category: Definition 3.1. A category C is the data of two collections. The first collection is called the objects of C and is denoted Obj(C). Given

More information

The ordering on permutations induced by continuous maps of the real line

The ordering on permutations induced by continuous maps of the real line Ergod. Th. & Dynam. Sys. (1987), 7, 155-160 Printed in Great Britain The ordering on permutations induced by continuous maps of the real line CHRIS BERNHARDT Department of Mathematics, Lafayette College,

More information

Computational Logic and Applications KRAKÓW On density of truth of infinite logic. Zofia Kostrzycka University of Technology, Opole, Poland

Computational Logic and Applications KRAKÓW On density of truth of infinite logic. Zofia Kostrzycka University of Technology, Opole, Poland Computational Logic and Applications KRAKÓW 2008 On density of truth of infinite logic Zofia Kostrzycka University of Technology, Opole, Poland By locally infinite logic, we mean a logic, which in some

More information

Lecture 2. (1) Every P L A (M) has a maximal element, (2) Every ascending chain of submodules stabilizes (ACC).

Lecture 2. (1) Every P L A (M) has a maximal element, (2) Every ascending chain of submodules stabilizes (ACC). Lecture 2 1. Noetherian and Artinian rings and modules Let A be a commutative ring with identity, A M a module, and φ : M N an A-linear map. Then ker φ = {m M : φ(m) = 0} is a submodule of M and im φ is

More information

Lecture Notes 17. Randomness: The verifier can toss coins and is allowed to err with some (small) probability if it is unlucky in its coin tosses.

Lecture Notes 17. Randomness: The verifier can toss coins and is allowed to err with some (small) probability if it is unlucky in its coin tosses. CS 221: Computational Complexity Prof. Salil Vadhan Lecture Notes 17 March 31, 2010 Scribe: Jonathan Ullman 1 Interactive Proofs ecall the definition of NP: L NP there exists a polynomial-time V and polynomial

More information

9 THEORY OF CODES. 9.0 Introduction. 9.1 Noise

9 THEORY OF CODES. 9.0 Introduction. 9.1 Noise 9 THEORY OF CODES Chapter 9 Theory of Codes After studying this chapter you should understand what is meant by noise, error detection and correction; be able to find and use the Hamming distance for a

More information

Functional Analysis MATH and MATH M6202

Functional Analysis MATH and MATH M6202 Functional Analysis MATH 36202 and MATH M6202 1 Inner Product Spaces and Normed Spaces Inner Product Spaces Functional analysis involves studying vector spaces where we additionally have the notion of

More information

Causal Consistency for Geo-Replicated Cloud Storage under Partial Replication

Causal Consistency for Geo-Replicated Cloud Storage under Partial Replication Causal Consistency for Geo-Replicated Cloud Storage under Partial Replication Min Shen, Ajay D. Kshemkalyani, TaYuan Hsu University of Illinois at Chicago Min Shen, Ajay D. Kshemkalyani, TaYuan Causal

More information

Introduction and basic definitions

Introduction and basic definitions Chapter 1 Introduction and basic definitions 1.1 Sample space, events, elementary probability Exercise 1.1 Prove that P( ) = 0. Solution of Exercise 1.1 : Events S (where S is the sample space) and are

More information

Discrete Fixpoint Approximation Methods in Program Static Analysis

Discrete Fixpoint Approximation Methods in Program Static Analysis Discrete Fixpoint Approximation Methods in Program Static Analysis P. Cousot Département de Mathématiques et Informatique École Normale Supérieure Paris

More information

Coset Decomposition Method for Decoding Linear Codes

Coset Decomposition Method for Decoding Linear Codes International Journal of Algebra, Vol. 5, 2011, no. 28, 1395-1404 Coset Decomposition Method for Decoding Linear Codes Mohamed Sayed Faculty of Computer Studies Arab Open University P.O. Box: 830 Ardeya

More information

Introduction to Topology

Introduction to Topology Chapter 2 Introduction to Topology In this chapter, we will use the tools we developed concerning sequences and series to study two other mathematical objects: sets and functions. For definitions of set

More information

HW 4 SOLUTIONS. , x + x x 1 ) 2

HW 4 SOLUTIONS. , x + x x 1 ) 2 HW 4 SOLUTIONS The Way of Analysis p. 98: 1.) Suppose that A is open. Show that A minus a finite set is still open. This follows by induction as long as A minus one point x is still open. To see that A

More information

SMV the Symbolic Model Verifier. Example: the alternating bit protocol. LTL Linear Time temporal Logic

SMV the Symbolic Model Verifier. Example: the alternating bit protocol. LTL Linear Time temporal Logic Model Checking (I) SMV the Symbolic Model Verifier Example: the alternating bit protocol LTL Linear Time temporal Logic CTL Fixed Points Correctness Slide 1 SMV - Symbolic Model Verifier SMV - Symbolic

More information

Electrical Circuits I

Electrical Circuits I Electrical Circuits I This lecture discusses the mathematical modeling of simple electrical linear circuits. When modeling a circuit, one ends up with a set of implicitly formulated algebraic and differential

More information

Game-Theoretic Foundations for Norms

Game-Theoretic Foundations for Norms Game-Theoretic Foundations for Norms Guido Boella Dipartimento di Informatica Università di Torino-Italy E-mail: guido@di.unito.it Leendert van der Torre Department of Computer Science University of Luxembourg

More information

The Geometric Distribution

The Geometric Distribution MATH 382 The Geometric Distribution Dr. Neal, WKU Suppose we have a fixed probability p of having a success on any single attempt, where p > 0. We continue to make independent attempts until we succeed.

More information

Computational Integer Programming. Lecture 2: Modeling and Formulation. Dr. Ted Ralphs

Computational Integer Programming. Lecture 2: Modeling and Formulation. Dr. Ted Ralphs Computational Integer Programming Lecture 2: Modeling and Formulation Dr. Ted Ralphs Computational MILP Lecture 2 1 Reading for This Lecture N&W Sections I.1.1-I.1.6 Wolsey Chapter 1 CCZ Chapter 2 Computational

More information

Formal Epistemology: Lecture Notes. Horacio Arló-Costa Carnegie Mellon University

Formal Epistemology: Lecture Notes. Horacio Arló-Costa Carnegie Mellon University Formal Epistemology: Lecture Notes Horacio Arló-Costa Carnegie Mellon University hcosta@andrew.cmu.edu Logical preliminaries Let L 0 be a language containing a complete set of Boolean connectives, including

More information

On Model Checking for Visibly Pushdown Automata

On Model Checking for Visibly Pushdown Automata Japan Institute of Advanced Industrial Science and Technology Research Center for Specification and Verification LATA 2012 On Model Checking for Visibly Pushdown Automata Nguyen Van Tang and Hitoshi Ohsaki

More information

Decentralized Control of Discrete Event Systems with Bounded or Unbounded Delay Communication 1

Decentralized Control of Discrete Event Systems with Bounded or Unbounded Delay Communication 1 Decentralized Control of Discrete Event Systems with Bounded or Unbounded Delay Communication 1 Stavros Tripakis 2 VERIMAG Technical Report TR-2004-26 November 2004 Abstract We introduce problems of decentralized

More information

Path Testing and Test Coverage. Chapter 9

Path Testing and Test Coverage. Chapter 9 Path Testing and Test Coverage Chapter 9 Structural Testing Also known as glass/white/open box testing Structural testing is based on using specific knowledge of the program source text to define test

More information

Path Testing and Test Coverage. Chapter 9

Path Testing and Test Coverage. Chapter 9 Path Testing and Test Coverage Chapter 9 Structural Testing Also known as glass/white/open box testing Structural testing is based on using specific knowledge of the program source text to define test

More information

Numerical Sequences and Series

Numerical Sequences and Series Numerical Sequences and Series Written by Men-Gen Tsai email: b89902089@ntu.edu.tw. Prove that the convergence of {s n } implies convergence of { s n }. Is the converse true? Solution: Since {s n } is

More information

Conditional Logic and Belief Revision

Conditional Logic and Belief Revision Conditional Logic and Belief Revision Ginger Schultheis (vks@mit.edu) and David Boylan (dboylan@mit.edu) January 2017 History The formal study of belief revision grew out out of two research traditions:

More information

Compiler Design. Spring Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro Diniz

Compiler Design. Spring Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro Diniz Compiler Design Spring 2010 Lexical Analysis Sample Exercises and Solutions Prof. Pedro Diniz USC / Information Sciences Institute 4676 Admiralty Way, Suite 1001 Marina del Rey, California 90292 pedro@isi.edu

More information

Parallel Programming in C with MPI and OpenMP

Parallel Programming in C with MPI and OpenMP Parallel Programming in C with MPI and OpenMP Michael J. Quinn Chapter 13 Finite Difference Methods Outline n Ordinary and partial differential equations n Finite difference methods n Vibrating string

More information

Basic System and Subsystem Structures in the Dataflow Algebra. A. J. Cowling

Basic System and Subsystem Structures in the Dataflow Algebra. A. J. Cowling Verification Testing Research Group, Department of Computer Science, University of Sheffield, Regent Court, 211, Portobello Street, Sheffield, S1 4DP, United Kingdom Email: A.Cowling @ dcs.shef.ac.uk Telephone:

More information

A comparison of sequencing formulations in a constraint generation procedure for avionics scheduling

A comparison of sequencing formulations in a constraint generation procedure for avionics scheduling A comparison of sequencing formulations in a constraint generation procedure for avionics scheduling Department of Mathematics, Linköping University Jessika Boberg LiTH-MAT-EX 2017/18 SE Credits: Level:

More information

MTAT Complexity Theory December 8th, Lecture 12

MTAT Complexity Theory December 8th, Lecture 12 MTAT.07.004 Complexity Theory December 8th, 2011 Lecturer: Peeter Laud Lecture 12 Scribe(s): Ilya Kuzovkin Introduction On the previous lecture we had a look onto interactive proofs, where the system consists

More information

2. Introduction to commutative rings (continued)

2. Introduction to commutative rings (continued) 2. Introduction to commutative rings (continued) 2.1. New examples of commutative rings. Recall that in the first lecture we defined the notions of commutative rings and field and gave some examples of

More information

DISCRETE MATHEMATICS W W L CHEN

DISCRETE MATHEMATICS W W L CHEN DISCRETE MATHEMATICS W W L CHEN c W W L Chen, 1991, 2008. This chapter is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or

More information

Wireless Network Security Spring 2016

Wireless Network Security Spring 2016 Wireless Network Security Spring 2016 Patrick Tague Class #3 Project Discussion; OMNET++ Intro 2016 Patrick Tague 1 Waitlists If you're currently registered for this class, but not planning to stay: please

More information

1 Recap: Interactive Proofs

1 Recap: Interactive Proofs Theoretical Foundations of Cryptography Lecture 16 Georgia Tech, Spring 2010 Zero-Knowledge Proofs 1 Recap: Interactive Proofs Instructor: Chris Peikert Scribe: Alessio Guerrieri Definition 1.1. An interactive

More information

Cyclops Tensor Framework

Cyclops Tensor Framework Cyclops Tensor Framework Edgar Solomonik Department of EECS, Computer Science Division, UC Berkeley March 17, 2014 1 / 29 Edgar Solomonik Cyclops Tensor Framework 1/ 29 Definition of a tensor A rank r

More information

On hyperconnected topological spaces

On hyperconnected topological spaces An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, 2016, f. 2, vol. 1 On hyperconnected topological spaces Vinod Kumar Devender Kumar Kamboj Received: 4.X.2012 / Accepted: 12.XI.2012 Abstract It

More information

Report 1 The Axiom of Choice

Report 1 The Axiom of Choice Report 1 The Axiom of Choice By Li Yu This report is a collection of the material I presented in the first round presentation of the course MATH 2002. The report focuses on the principle of recursive definition,

More information

Methods for the specification and verification of business processes MPB (6 cfu, 295AA)

Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 20 - Workflow modules 1 Object We study Workflow modules to model interaction

More information

1 More finite deterministic automata

1 More finite deterministic automata CS 125 Section #6 Finite automata October 18, 2016 1 More finite deterministic automata Exercise. Consider the following game with two players: Repeatedly flip a coin. On heads, player 1 gets a point.

More information

Ability to Count Messages Is Worth Θ( ) Rounds in Distributed Computing

Ability to Count Messages Is Worth Θ( ) Rounds in Distributed Computing Ability to Count Messages Is Worth Θ( ) Rounds in Distributed Computing Tuomo Lempiäinen Aalto University, Finland LICS 06 July 7, 06 @ New York / 0 Outline Introduction to distributed computing Different

More information

Theoretical Foundations of the UML

Theoretical Foundations of the UML Theoretical Foundations of the UML Lecture 17+18: A Logic for MSCs Joost-Pieter Katoen Lehrstuhl für Informatik 2 Software Modeling and Verification Group moves.rwth-aachen.de/teaching/ws-1718/fuml/ 5.

More information

Definite Logic Programs

Definite Logic Programs Chapter 2 Definite Logic Programs 2.1 Definite Clauses The idea of logic programming is to use a computer for drawing conclusions from declarative descriptions. Such descriptions called logic programs

More information

A Note on Turing Machine Design

A Note on Turing Machine Design CS103 Handout 17 Fall 2013 November 11, 2013 Problem Set 7 This problem explores Turing machines, nondeterministic computation, properties of the RE and R languages, and the limits of RE and R languages.

More information

Lecture 6: Introducing Complexity

Lecture 6: Introducing Complexity COMP26120: Algorithms and Imperative Programming Lecture 6: Introducing Complexity Ian Pratt-Hartmann Room KB2.38: email: ipratt@cs.man.ac.uk 2015 16 You need this book: Make sure you use the up-to-date

More information

Distributed Systems Byzantine Agreement

Distributed Systems Byzantine Agreement Distributed Systems Byzantine Agreement He Sun School of Informatics University of Edinburgh Outline Finish EIG algorithm for Byzantine agreement. Number-of-processors lower bound for Byzantine agreement.

More information

Ma/CS 6b Class 24: Error Correcting Codes

Ma/CS 6b Class 24: Error Correcting Codes Ma/CS 6b Class 24: Error Correcting Codes By Adam Sheffer Communicating Over a Noisy Channel Problem. We wish to transmit a message which is composed of 0 s and 1 s, but noise might accidentally flip some

More information

Duality in Logic Programming

Duality in Logic Programming Syracuse University SURFACE Electrical Engineering and Computer Science Technical Reports College of Engineering and Computer Science 3-1991 Duality in Logic Programming Feng Yang Follow this and additional

More information

Snapshots. Chandy-Lamport Algorithm for the determination of consistent global states <$1000, 0> <$50, 2000> mark. (order 10, $100) mark

Snapshots. Chandy-Lamport Algorithm for the determination of consistent global states <$1000, 0> <$50, 2000> mark. (order 10, $100) mark 8 example: P i P j (5 widgets) (order 10, $100) cji 8 ed state P i : , P j : , c ij : , c ji : Distributed Systems

More information

The purpose of this report is to recommend a Geographic Information System (GIS) Strategy for the Town of Richmond Hill.

The purpose of this report is to recommend a Geographic Information System (GIS) Strategy for the Town of Richmond Hill. Staff Report for Committee of the Whole Meeting Department: Division: Subject: Office of the Chief Administrative Officer Strategic Initiatives SRCAO.18.12 GIS Strategy Purpose: The purpose of this report

More information