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We survey recent progress in the development of mathematical techniques for specifying and verifying complex hardware and software systems. Many of these techniques are capable of handling industrial-sized examples; in fact, in some cases these techniques are already being used on a regular basis in industry. Success in formal specification can be attributed to notations that are accessible to system designers and to new methodologies for applying these notations effectively. Success in verification can be attributed to the development of new tools such as more powerful theorem provers and model checkers than were previously available. Finally, we suggest some general research directions that we believe are likely to lead to technological advances. Although it is difficult to predict where the future advances will come, optimism about the next generation of formal methods is justified in view of the progress during the past decade. Such progress, however, will strongly depend on continued support for basic research on new specification languages and new verification techniques.

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