Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

From the Book:
“Clean code that works” is Ron Jeffries’ pithy phrase. The goal is clean code that works, and for a whole bunch of reasons:
Clean code that works is a predictable way to develop. You know when you are finished, without having to worry about a long bug trail.Clean code that works gives you a chance to learn all the lessons that the code has to teach you. If you only ever slap together the first thing you think of, you never have time to think of a second, better, thing. Clean code that works improves the lives of users of our software.Clean code that works lets your teammates count on you, and you on them.Writing clean code that works feels good.But how do you get to clean code that works? Many forces drive you away from clean code, and even code that works. Without taking too much counsel of our fears, here’s what we do—drive development with automated tests, a style of development called “Test-Driven Development” (TDD for short). 
In Test-Driven Development, you:
Write new code only if you first have a failing automated test.Eliminate duplication.

Two simple rules, but they generate complex individual and group behavior. Some of the technical implications are:You must design organically, with running code providing feedback between decisionsYou must write your own tests, since you can’t wait twenty times a day for someone else to write a testYour development environment must provide rapid response to small changesYour designs must consist of many highly cohesive, loosely coupled components, just to make testing easy

The two rules imply an order to the tasks ofprogramming:
1. Red—write a little test that doesn’t work, perhaps doesn’t even compile at first
2. Green—make the test work quickly, committing whatever sins necessary in the process
3. Refactor—eliminate all the duplication created in just getting the test to work


Red/green/refactor. The TDD’s mantra.

Assuming for the moment that such a style is possible, it might be possible to dramatically reduce the defect density of code and make the subject of work crystal clear to all involved. If so, writing only code demanded by failing tests also has social implications:
If the defect density can be reduced enough, QA can shift from reactive to pro-active workIf the number of nasty surprises can be reduced enough, project managers can estimate accurately enough to involve real customers in daily developmentIf the topics of technical conversations can be made clear enough, programmers can work in minute-by-minute collaboration instead of daily or weekly collaborationAgain, if the defect density can be reduced enough, we can have shippable software with new functionality every day, leading to new business relationships with customers


So, the concept is simple, but what’s my motivation? Why would a programmer take on the additional work of writing automated tests? Why would a programmer work in tiny little steps when their mind is capable of great soaring swoops of design? Courage.
Courage
Test-driven development is a way of managing fear during programming. I don’t mean fear in a bad way, pow widdle prwogwammew needs a pacifiew, but fear in the legitimate, this-is-a-hard-problem-and-I-can’t-see-the-end-from-the-beginning sense. If pain is nature’s way of saying “Stop!”, fear is nature’s way of saying “Be careful.” Being careful is good, but fear has a host of other effects:
Makes you tentativeMakes you want to communicate lessMakes you shy from feedbackMakes you grumpy

None of these effects are helpful when programming, especially when programming something hard. So, how can you face a difficult situation and:
Instead of being tentative, begin learning concretely as quickly as possible.Instead of clamming up, communicate more clearly.Instead of avoiding feedback, search out helpful, concrete feedback.(You’ll have to work on grumpiness on your own.) 

Imagine programming as turning a crank to pull a bucket of water from a well. When the bucket is small, a free-spinning crank is fine. When the bucket is big and full of water, you’re going to get tired before the bucket is all the way up. You need a ratchet mechanism to enable you to rest between bouts of cranking. The heavier the bucket, the closer the teeth need to be on the ratchet.

The tests in test-driven development are the teeth of the ratchet. Once you get one test working, you know it is working, now and forever. You are one step closer to having everything working than you were when the test was broken. Now get the next one working, and the next, and the next. By analogy, the tougher the programming problem, the less ground should be covered by each test.

Readers of Extreme Programming Explained will notice a difference in tone between XP and TDD. TDD isn’t an absolute like Extreme Programming. XP says, “Here are things you must be able to do to be prepared to evolve further.” TDD is a little fuzzier. TDD is an awareness of the gap between decision and feedback during programming, and techniques to control that gap. “What if I do a paper design for a week, then test-drive the code? Is that TDD?” Sure, it’s TDD. You were aware of the gap between decision and feedback and you controlled the gap deliberately.

That said, most people who learn TDD find their programming practice changed for good. “Test Infected” is the phrase Erich Gamma coined to describe this shift. You might find yourself writing more tests earlier, and working in smaller steps than you ever dreamed would be sensible. On the other hand, some programmers learn TDD and go back to their earlier practices, reserving TDD for special occasions when ordinary programming isn’t making progress.

There are certainly programming tasks that can’t be driven solely by tests (or at least, not yet). Security software and concurrency, for example, are two topics where TDD is not sufficient to mechanically demonstrate that the goals of the software have been met. Security relies on essentially defect-free code, true, but also on human judgement about the methods used to secure the software. Subtle concurrency problems can’t be reliably duplicated by running the code.

Once you are finished reading this book, you should be ready to:
Start simplyWrite automated testsRefactor to add design decisions one at a time

This book is organized into three sections.
An example of writing typical model code using TDD. The example is one I got from Ward Cunningham years ago, and have used many times since, multi-currency arithmetic. In it you will learn to write tests before code and grow a design organically.An example of testing more complicated logic, including reflection and exceptions, by developing a framework for automated testing. This example also serves to introduce you to the xUnit architecture that is at the heart of many programmer-oriented testing tools. In the second example you will learn to work in even smaller steps than in the first example, including the kind of self-referential hooha beloved of computer scientists.Patterns for TDD. Included are patterns for the deciding what tests to write, how to write tests using xUnit, and a greatest hits selection of the design patterns and refactorings used in the examples.

I wrote the examples imagining a pair programming session. If you like looking at the map before wandering around, you may want to go straight to the patterns in Section 3 and use the examples as illustrations. If you prefer just wandering around and then looking at the map to see where you’ve been, try reading the examples through and refering to the patterns when you want more detail about a technique, then using the patterns as a reference.

Several reviewers have commented they got the most out of the examples when they started up a programming environment and entered the code and ran the tests as they read.

A note about the examples. Both examples, multi-currency calculation and a testing framework, appear simple. There are (and I have seen) complicated, ugly, messy ways of solving the same problems. I could have chosen one of those complicated, ugly, messy solutions to give the book an air of “reality.” However, my goal, and I hope your goal, is to write clean code that works. Before teeing off on the examples as being too simple, spend 15 seconds imagining a programming world in which all code was this clear and direct, where there were no complicated solutions, only apparently complicated problems begging for careful thought. TDD is a practice that can help you lead yourself to exactly that careful thought.

Test Driven Development: By Example

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

http://user.it.uu.se/~jarst116/slides/week4.pdf

Graph-Based Algorithms for Boolean Function Manipulation

We consider a fully SAT-based method of unbounded symbolic model checking based on computing Craig interpolants. In benchmark studies using a set of large industrial circuit verification instances, this method is greatly more efficient than BDD-based symbolic model checking, and compares favorably to some recent SAT-based model checking methods on positive instances.

Interpolation and SAT-based model checking

Synthesis of reversible logic has become an active research area in the last years. But many proposed algorithms are evaluated with a small set of benchmarks only. Furthermore, results are often documented only in terms of gate counts or quantum costs, rather than presenting the specific circuit. In this paper RevLib (www.revlib.org) is introduced, an online resource for reversible functions and reversible circuits. RevLib provides a large database of functions with respective circuit realizations. RevLib is designed to ease the evaluation of new methods and facilitate the comparison of results. In addition, tools are introduced to support researchers in evaluating their algorithms and documenting their results.

/pdf/revlib-an-online-resource-for-reversible-functions-and-30pwkwl5gp.pdf

RevLib: An Online Resource for Reversible Functions and Reversible Circuits

Reversible logic is the basis for several emerging technologies such as quantum computing, optical computing, or DNA computing and has further applications in domains like low-power design and nanotechnologies. However, current methods for the synthesis of reversible logic are limited, i.e. they are applicable to relatively small functions only. In this paper, we propose a synthesis approach, that can cope with Boolean functions containing more than a hundred of variables. We present a technique to derive reversible circuits for a function given by a Binary Decision Diagram (BDD). The circuit is obtained using an algorithm with linear worst case behavior regarding run-time and space requirements. Furthermore, the size of the resulting circuit is bounded by the BDD size. This allows to transfer theoretical results known from BDDs to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.

/pdf/bdd-based-synthesis-of-reversible-logic-for-large-functions-4v6eu4lnnf.pdf

BDD-based synthesis of reversible logic for large functions

In the past years, quantum computers more and more have evolved from an academic idea to an upcoming reality. IBM’s project IBM ${Q}$ can be seen as evidence of this progress. Launched in March 2017 with the goal to provide access to quantum computers for a broad audience, this allowed users to conduct quantum experiments on a 5-qubit and, since June 2017, also on a 16-qubit quantum computer (called IBM QX2 and IBM QX3, respectively). Revised versions of these 5- and 16-qubit quantum computers (named IBM QX4 and IBM QX5, respectively) are available since September 2017. In order to use these, the desired quantum functionality (e.g., provided in terms of a quantum circuit) has to be properly mapped so that the underlying physical constraints are satisfied—a complex task. This demands solutions to automatically and efficiently conduct this mapping process. In this paper, we propose a methodology which addresses this problem, i.e., maps the given quantum functionality to a realization which satisfies all constraints given by the architecture and, at the same time, keeps the overhead in terms of additionally required quantum gates minimal. The proposed methodology is generic, can easily be configured for similar future architectures, and is fully integrated into IBM’s SDK. Experimental evaluations show that the proposed approach clearly outperforms IBM’s own mapping solution. In fact, for many quantum circuits, the proposed approach determines a mapping to the IBM architecture within minutes, while IBM’s solution suffers from long runtimes and runs into a timeout of 1 h in several cases. As an additional benefit, the proposed approach yields mapped circuits with smaller costs (i.e., fewer additional gates are required). All implementations of the proposed methodology are publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping .

An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures

While a couple of impressive quantum technologies have been proposed, they have several intrinsic limitations which must be considered by circuit designers to produce realizable circuits. Limited interaction distance between gate qubits is one of the most common limitations. In this paper, we suggest extensions of the existing synthesis flow aimed to realize circuits for quantum architectures with linear nearest neighbor interaction. To this end, a template matching optimization, an exact synthesis approach, and two reordering strategies are introduced. The proposed methods are combined as an integrated synthesis flow. Experiments show that by using the suggested flow, quantum cost can be improved by more than 50% on average.

Synthesis of quantum circuits for linear nearest neighbor architectures

Synthesis of reversible logic has become a very important research area in recent years. Applications can be found in the domain of low-power design, optical computing, and quantum computing. In the past, several approaches have been introduced that synthesize reversible networks with respect to a given function. Most of these methods only approximate a minimal network representation. In this paper, exact algorithms for the synthesis of multiple-control Toffoli networks are presented, i.e., algorithms that guarantee to find a network with the minimal number of gates. Our iterative algorithms formulate the synthesis problem as a sequence of decision problems. The decision problems are encoded as Boolean satisfiability (SAT) or SAT modulo theory (SMT) instances, respectively. As soon as one of these instances becomes satisfiable, a Toffoli network representation for the given function has been found. We show that choosing the encoding for synthesis is crucial for the resulting runtimes. Furthermore, we discuss the principal limits of the SAT and SMT approaches. To overcome these limits, we propose a method using problem-specific knowledge during synthesis. In addition, better embeddings to make irreversible functions reversible are considered. For the resulting synthesis problems, an improvement is presented that reduces the overall runtime by automatically setting the constant inputs to their optimal values. Experimental results on a large set of benchmarks demonstrate the differences between three exact synthesis algorithms. In addition, a comparison with the best-known heuristic results is provided. In summary, the results show that, for some benchmarks, the heuristic approaches have already found the minimal network, while for other benchmarks, significantly smaller networks exist.

Robert Wille

Papers

RevLib: An Online Resource for Reversible Functions and Reversible Circuits

BDD-based synthesis of reversible logic for large functions

An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures

Synthesis of quantum circuits for linear nearest neighbor architectures

Exact Multiple-Control Toffoli Network Synthesis With SAT Techniques