This book grew out of a NATO Advanced Study Institute summer school that was held in Antalya, TUrkey from 26 May to 6 June 1997. The purpose of the summer school was to expose recent advances in the formal verification of systems composed of both logical and continuous time components. The course was structured in two parts. The first part covered theorem-proving, system automaton models, logics, tools, and complexity of verification. The second part covered modeling and verification of hybrid systems, i. e., systems composed of a discrete event part and a continuous time part that interact with each other in novel ways. Along with advances in microelectronics, methods to design and build logical systems have grown progressively complex. One way to tackle the problem of ensuring the error-free operation of digital or hybrid systems is through the use of formal techniques. The exercise of comparing the formal specification of a logical system namely, what it is supposed to do to its formal operational description-what it actually does!-in an automated or semi-automated manner is called verification. Verification can be performed in an after-the-fact manner, meaning that after a system is already designed, its specification and operational description are regenerated or modified, if necessary, to match the verification tool at hand and the consistency check is carried out.

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