Amir Pnueli

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.

This book is about the verification of reactive systems. A reactive system is a system that maintains an ongoing interaction with its environment, as opposed to computing some final value on termination. The family of reactive systems includes many classes of programs whose correct and reliable construction is con­ sidered to be particularly challenging, including concurrent programs, embedded and process control programs, and operating systems. Typical examples of such systems are an air traffic control system, programs controlling mechanical devices such as a train, or perpetually ongoing processes such as a nuclear reactor. With the expanding use of computers in safety-critical areas, where failure is potentially disastrous, correctness is crucial. This has led to the introduction of formal verification techniques, which give both users and designers of software and hardware systems greater confidence that the systems they build meet the desired specifications. Framework The approach promoted in this book is based on the use of temporal logic for specifying properties of reactive systems, and develops an extensive verification methodology for proving that a system meets its temporal specification. Reactive programs must be specified in terms of their ongoing behavior, and temporal logic provides an expressive and natural language for specifying this behavior. Our framework for specifying and verifying temporal properties of reactive systems is based on the following four components: 1. A computational model to describe the behavior of reactive systems. The model adopted in this book is that of a Fair Transition System (FTS).

HIS BOOK CONTAINS a most comprehensive text that presents syntax-directed and compositional methods for the formal veri?- T cation of programs. The approach is not language-bounded in the sense that it covers a large variety of programming models and features that appear in most modern programming languages. It covers the classes of - quential and parallel, deterministic and non-deterministic, distributed and object-oriented programs. For each of the classes it presents the various c- teria of correctness that are relevant for these classes, such as interference freedom, deadlock freedom, and appropriate notions of liveness for parallel programs. Also, special proof rules appropriate for each class of programs are presented. In spite of this diversity due to the rich program classes cons- ered, there exist a uniform underlying theory of veri?cation which is synt- oriented and promotes compositional approaches to veri?cation, leading to scalability of the methods. The text strikes the proper balance between mathematical rigor and - dactic introduction of increasingly complex rules in an incremental manner, adequately supported by state-of-the-art examples. As a result it can serve as a textbook for a variety of courses on di?erent levels and varying durations. It can also serve as a reference book for researchers in the theory of veri?- tion, in particular since it contains much material that never before appeared in book form. This is specially true for the treatment of object-oriented p- grams which is entirely novel and is strikingly elegant.

HIS BOOK CONTAINS a most comprehensive text that presents syntax-directed and compositional methods for the formal veri?- T cation of programs. The approach is not language-bounded in the sense that it covers a large variety of programming models and features that appear in most modern programming languages. It covers the classes of - quential and parallel, deterministic and non-deterministic, distributed and object-oriented programs. For each of the classes it presents the various c- teria of correctness that are relevant for these classes, such as interference freedom, deadlock freedom, and appropriate notions of liveness for parallel programs. Also, special proof rules appropriate for each class of programs are presented. In spite of this diversity due to the rich program classes cons- ered, there exist a uniform underlying theory of veri?cation which is synt- oriented and promotes compositional approaches to veri?cation, leading to scalability of the methods. The text strikes the proper balance between mathematical rigor and - dactic introduction of increasingly complex rules in an incremental manner, adequately supported by state-of-the-art examples. As a result it can serve as a textbook for a variety of courses on di?erent levels and varying durations. It can also serve as a reference book for researchers in the theory of veri?- tion, in particular since it contains much material that never before appeared in book form. This is specially true for the treatment of object-oriented p- grams which is entirely novel and is strikingly elegant.

This book is about the verification of reactive systems. A reactive system is a system that maintains an ongoing interaction with its environment, as opposed to computing some final value on termination. The family of reactive systems includes many classes of programs whose correct and reliable construction is con­ sidered to be particularly challenging, including concurrent programs, embedded and process control programs, and operating systems. Typical examples of such systems are an air traffic control system, programs controlling mechanical devices such as a train, or perpetually ongoing processes such as a nuclear reactor. With the expanding use of computers in safety-critical areas, where failure is potentially disastrous, correctness is crucial. This has led to the introduction of formal verification techniques, which give both users and designers of software and hardware systems greater confidence that the systems they build meet the desired specifications. Framework The approach promoted in this book is based on the use of temporal logic for specifying properties of reactive systems, and develops an extensive verification methodology for proving that a system meets its temporal specification. Reactive programs must be specified in terms of their ongoing behavior, and temporal logic provides an expressive and natural language for specifying this behavior. Our framework for specifying and verifying temporal properties of reactive systems is based on the following four components: 1. A computational model to describe the behavior of reactive systems. The model adopted in this book is that of a Fair Transition System (FTS).

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.