This chapter introduces test criteria based on logical expressions. While logic coverage criteria have been known for a long time, their use has been steadily growing in recent years. One cause for their use in practice has been their incorporation in standards such as those accepted by the US Federal Aviation Administration (FAA) for safety critical avionics software in commercial aircraft. As in Chapter 2, we start with a sound theoretical foundation for logic predicates and clauses with the goal of making the subsequent testing criteria simpler. As before, we take a generic view of the structures and criteria, then discuss how logic expressions can be derived from various software artifacts, including code, specifications, and finite state machines.

Readers who are already familiar with some of the common criteria may have difficulty recognizing them at first. This is because we introduce a generic collection of test criteria, and thus choose names that best help articulate all of the criteria. That is, we are abstracting a number of existing criteria that are closely related, yet use conflicting terminology.

OVERVIEW: LOGIC PREDICATES AND CLAUSES

We formalize logical expressions in a common mathematical way. A predicate is an expression that evaluates to a boolean value, and is our topmost structure. A simple example is: ((a > b) ∨ C) ∧ p(x). Predicates may contain boolean variables, non-boolean variables that are compared with the comparator operators {>, <, =, ≥, ≤, ≠}, and function calls.

This chapter introduces the major test coverage criteria in use today. It starts out in a very theoretical way, but a firm grasp of the theoretical aspects of graphs and graph coverage makes the remainder of the chapter simpler. We first emphasize a generic view of a graph without regard to the graph's source. After this model is established, the rest of the chapter turns to practical applications by demonstrating how graphs can be obtained from various software artifacts and how the generic versions of the criteria are adapted to those graphs.

OVERVIEW

Directed graphs form the foundation for many coverage criteria. Given an artifact under test, the idea is to obtain a graph abstraction of that artifact. For example, the most common graph abstraction for source code maps code to a control flow graph. It is important to understand that the graph is not the same as the artifact, and that, indeed, artifacts typically have several useful, but nonetheless quite different, graph abstractions. The same abstraction that produces the graph from the artifact also maps test cases for the artifact to paths in the graph. Accordingly, a graphbased coverage criterion evaluates a test set for an artifact in terms of how the paths corresponding to the test cases “cover” the artifact's graph abstraction.

We give our basic notion of a graph below and will add additional structures later in the chapter when needed.

The ideas and techniques of software testing have become essential knowledge for all software developers. A software developer can expect to use the concepts presented in this book many times during his or her career. This chapter introduces the subject of software testing by describing the activities of a test engineer, defining a number of key terms, and then explaining the central notion of test coverage.

Software is a key ingredient in many of the devices and systems that pervade our society. Software defines the behavior of network routers, financial networks, telephone switching networks, the Web, and other infrastructure of modern life. Software is an essential component of embedded applications that control exotic applications such as airplanes, spaceships, and air traffic control systems, as well as mundane appliances such as watches, ovens, cars, DVD players, garage door openers, cell phones, and remote controllers. Modern households have over 50 processors, and some new cars have over 100; all of them running software that optimistic consumers assume will never fail! Although many factors affect the engineering of reliable software, including, of course, careful design and sound process management, testing is the primary method that the industry uses to evaluate software under development. Fortunately, a few basic software testing concepts can be used to design tests for a large variety of software applications. A goal of this book is to present these concepts in such a way that the student or practicing engineer can easily apply them to any software testing situation.

In previous chapters, we learned how to generate tests from graphs, logical expressions, and partitions of the input space. A fourth major source for test coverage criteria is syntactic descriptions of software artifacts. As with graphs and logical expressions, several types of artifacts can be used, including source and input requirements.

The essential characteristic of syntax-based testing is that a syntactic description such as a grammar or BNF is used. Chapters 2 and 3 discussed how to build graph models and logic models from artifacts such as the program, design descriptions, and specifications. Chapter 4 discussed how to build a model of the inputs based on some description of the input space. Then test criteria were applied to the models. With syntax-based testing, however, the syntax of the software artifact is used as the model and tests are created from the syntax.

SYNTAX-BASED COVERAGE CRITERIA

Syntax structures can be used for testing in several ways. We can use the syntax to generate artifacts that are valid (correct syntax), or artifacts that are invalid (incorrect syntax). Sometimes the structures we generate are test cases themselves, and sometimes they are used to help us find test cases. We explore these differences in the subsections of this chapter. As usual, we begin by defining general criteria on syntactic structures and then make them specific to specific artifacts.

BNF Coverage Criteria

It is very common in software engineering to use structures from automata theory to describe the syntax of software artifacts.

In a very fundamental way, all testing is about choosing elements from the input space of the software being tested. The criteria presented previously can be viewed as defining ways to divide the input space according to the test requirements. The assumption is that any collection of values that satisfies the same test requirement will be “just as good.” Input space partitioning takes that view in a much more direct way. The input domain is defined in terms of the possible values that the input parameters can have. The input parameters can be method parameters and global variables, objects representing current state, or user-level inputs to a program, depending on what kind of software artifact is being analyzed. The input domain is then partitioned into regions that are assumed to contain equally useful values from a testing perspective, and values are selected from each region.

This way of testing has several advantages. It is fairly easy to get started because it can be applied with no automation and very little training. The tester does not need to understand the implementation; everything is based on a description of the inputs. It is also simple to “tune” the technique to get more or fewer tests.

Consider an abstract partition q over some domain D. The partition q defines a set of equivalence classes, which we simply call blocks, Bq.

This book presents software testing as a practical engineering activity, essential to producing high-quality software. It is designed to be used as the primary textbook in either an undergraduate or graduate course on software testing, as a supplement to a general course on software engineering or data structures, and as a resource for software test engineers and developers. This book has a number of unique features:

• It organizes the complex and confusing landscape of test coverage criteria with a novel and extremely simple structure. At a technical level, software testing is based on satisfying coverage criteria. The book's central observation is that there are few truly different coverage criteria, each of which fits easily into one of four categories: graphs, logical expressions, input space, and syntax structures. This not only simplifies testing, but it also allows a convenient and direct theoretical treatment of each category. This approach contrasts strongly with the traditional view of testing, which treats testing at each phase in the development process differently.

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