There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

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Principles of Model Checking

Model Checking

In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers.



Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others.



The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference.



The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.


Table of Contents

1 Introduction 
2 Modelling I; Synchronous Network Model 
3 Leader Election in a Synchronous Ring 
4 Algorithms in General Synchronous Networks 
5 Distributed Consensus with Link Failures 
6 Distributed Consensus with Process Failures 
7 More Consensus Problems 
8 Modelling II: Asynchronous System Model 
9 Modelling III: Asynchronous Shared Memory Model 
10 Mutual Exclusion 
11 Resource Allocation 
12 Consensus 
13 Atomic Objects 
14 Modelling IV: Asynchronous Network Model 
15 Basic Asynchronous Network Algorithms 
16 Synchronizers 
17 Shared Memory versus Networks 
18 Logical Time 
19 Global Snapshots and Stable Properties 
20 Network Resource Allocation 
21 Asynchronous Networks with Process Failures 
22 Data Link Protocols 
23 Partially Synchronous System Models 
24 Mutual Exclusion with Partial Synchrony 
25 Consensus with Partial Synchrony

Distributed algorithms

We present a logic for stating properties such as, "after a request for service there is at least a 98\045 probability that the service will be carried out within 2 seconds". The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabil- ities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satis- fies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and\003This research report is a revised and extended version of a paper that has appeared under the title "A Framework for Reasoning about Time and Reliability" in the Proceeding of the 10thIEEE Real-time Systems Symposium, Santa Monica CA, December 1989. This work was partially supported by the Swedish Board for Technical Development (STU) as part of Esprit BRA Project SPEC, and by the Swedish Telecommunication Administration.1the Markov chain. A simple example is included to illustrate the algorithms.

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A logic for reasoning about time and reability

Over the last few years there has been an increasing research effort directed towards the automatic verification of infinite state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems), which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a well-ordered and well-founded preorder such that the transition relation is "monotonic" (is a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: reachability; eventuality; and simulation. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.

General decidability theorems for infinite-state systems

Testing of Finite State Machines.- I. Testing of Finite State Machines.- 1 Homing and Synchronizing Sequences.- 2 State Identification.- 3 State Verification.- 4 Conformance Testing.- II. Testing of Labeled Transition Systems.- Testing of Labeled Transition Systems.- 5 Preorder Relations.- 6 Test Generation Algorithms Based on Preorder Relations.- 7 I/O-automata Based Testing.- 8 Test Derivation from Timed Automata.- 9 Testing Theory for Probabilistic Systems.- III. Model-Based Test Case Generation.- Model-Based Test Case Generation.- 10 Methodological Issues in Model-Based Testing.- 11 Evaluating Coverage Based Testing.- 12 Technology of Test-Case Generation.- 13 Real-Time and Hybrid Systems Testing.- IV. Tools and Case Studies.- Tools and Case Studies.- 14 Tools for Test Case Generation.- 15 Case Studies.- V. Standardized Test Notation and Execution Architecture.- Standardized Test Notation and Execution Architecture.- 16 TTCN-3.- 17 UML 2.0 Testing Profile.- VI. Beyond Testing.- Beyond Testing.- 18 Run-Time Verification.- 19 Model Checking.- VII. Appendices.- Appendices.- 20 Model-Based Testing - A Glossary.- 21 Finite State Machines.- 22 Labelled Transition Systems.

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Model-Based Testing of Reactive Systems, Advanced Lectures

The verification of a particular class of infinite-state systems, namely, systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels, is considered. This class is able to model, e.g., link protocols such as the Alternating Bit Protocol and HDLC. For this class of systems, it is shown that several interesting verification problems are decidable by giving algorithms for verifying: the reachability problem (whether a finite set of global states is reachable from some other global state of the system); the safety property over traces, formulated as regular sets of allowed finite traces; and eventuality properties (whether all computations of a system eventually reach a given set of states). The algorithms are used to verify some idealized sliding-window protocols with reasonable time and space resources. >

Verifying programs with unreliable channels

A formalism for specifying probabilistic transition systems, which constitute a basic semantic model for description and analysis of, e.g. reliability aspects of concurrent and distributed systems, is presented. The formalism itself is based on transition systems. Roughly a specification has the form of a transition system in which transitions are labeled by sets of allowed probabilities. A satisfaction relation between processes and specifications that generalizes probabilistic bisimulation equivalence is defined. It is shown that it is analogous to the extension from processes to modal transition systems given by K. Larsen and B. Thomsen (1988). Another weaker criterion views a specification as defining a set of probabilistic processes; refinement is then simply containment between sets of processes. A complete method for verifying containment between specifications, which extends methods for deciding containment between specifications, which extends methods for deciding containment between finite automata or tree acceptors, is presented. >

Bengt Jonsson

Papers

A logic for reasoning about time and reability

General decidability theorems for infinite-state systems

Model-Based Testing of Reactive Systems, Advanced Lectures

Verifying programs with unreliable channels

Specification and refinement of probabilistic processes