The use of mathematical methods in the development of software is essential when reliable systems are sought; in particular they are now strongly recommended by the official norms adopted in the production of critical software. Program Verification is the area of computer science that studies mathematical methods for checking that a program conforms to its specification. This text is a self-contained introduction to program verification using logic-based methods, presented in the broader context of formal methods for software engineering. The idea of specifying the behaviour of individual software components by attaching contracts to them is now a widely followed approach in program development, which has given rise notably to the development of a number of behavioural interface specification languages and program verification tools. A foundation for the static verification of programs based on contract-annotated routines is laid out in the book. These can be independently verified, which provides a modular approach to the verification of software. The text assumes only basic knowledge of standard mathematical concepts that should be familiar to any computer science student. It includes a self-contained introduction to propositional logic and first-order reasoning with theories, followed by a study of program verification that combines theoretical and practical aspects - from a program logic (a variant of Hoare logic for programs containing user-provided annotations) to the use of a realistic tool for the verification of C programs (annotated using the ACSL specification language), through the generation of verification conditions and the static verification of runtime errors.
Following the fall of the Melaka Sultanate to the Portuguese in 1511, the sultanates of Johor and Aceh emerged as major trading centers alongside Portuguese Melaka. Each power represented wider global interests. Aceh had links with Gujerat, the Ottoman Empire and the Levant. Johor was a center for Javanese merchants and others involved with the Eastern spice trade. Melaka was part of the Estado da India, Portugal's trading empire that extended from Japan to Mozambique. Throughout the sixteenth century, a peculiar balance among the three powers became an important character of the political and economical life in the Straits of Melaka. The arrival of the Dutch in the early seventeenth century upset the balance and led to the decline of Portuguese Melaka. Making extensive use of contemporary Portuguese sources, Paulo Pinto uses geopolitical approach to analyze the financial, political, economic and military institutions that underlay this triangular arrangement, a system that persisted because no one power could achieve an undisputed hegemony. He also considers the position of post-conquest Melaka in the Malay World, where it remained a symbolic center of Malay civilization and a model of Malay political authority despite changes associated with Portuguese rule. In the process provides information on the social, political and genealogical circumstances of the Johor and Aceh sultanates.
This volume clearly reflects Ricardo Mane's legacy, his contribution to mathematics and the diversity of his mathematical intersts. It contains fifteen refereed research papers on thems including Hamiltonian and Lagrangian dynamics, growth rate of the number of geodesics on a compact manifold, one dimensional complex and real dynamics, and bifurcations and singular cycles. This book also contains two famous sets of notes by Ricardo Mane. One is the seminal paper on Lagrangian dynamics that he had prepared for the conference; the other is on the genericity of zero exponents area preserving diffeomorphisms on surfaces when non Anosov. This book will be of particular interest to researchers and graduate students in mathematics, mechanics and mathematical physics.
Following the fall of the Melaka Sultanate to the Portuguese in 1511, the sultanates of Johor and Aceh emerged as major trading centers alongside Portuguese Melaka. Each power represented wider global interests. Aceh had links with Gujerat, the Ottoman Empire and the Levant. Johor was a center for Javanese merchants and others involved with the Eastern spice trade. Melaka was part of the Estado da India, Portugal's trading empire that extended from Japan to Mozambique. Throughout the sixteenth century, a peculiar balance among the three powers became an important character of the political and economical life in the Straits of Melaka. The arrival of the Dutch in the early seventeenth century upset the balance and led to the decline of Portuguese Melaka. Making extensive use of contemporary Portuguese sources, Paulo Pinto uses geopolitical approach to analyze the financial, political, economic and military institutions that underlay this triangular arrangement, a system that persisted because no one power could achieve an undisputed hegemony. He also considers the position of post-conquest Melaka in the Malay World, where it remained a symbolic center of Malay civilization and a model of Malay political authority despite changes associated with Portuguese rule. In the process provides information on the social, political and genealogical circumstances of the Johor and Aceh sultanates.
The use of mathematical methods in the development of software is essential when reliable systems are sought; in particular they are now strongly recommended by the official norms adopted in the production of critical software. Program Verification is the area of computer science that studies mathematical methods for checking that a program conforms to its specification. This text is a self-contained introduction to program verification using logic-based methods, presented in the broader context of formal methods for software engineering. The idea of specifying the behaviour of individual software components by attaching contracts to them is now a widely followed approach in program development, which has given rise notably to the development of a number of behavioural interface specification languages and program verification tools. A foundation for the static verification of programs based on contract-annotated routines is laid out in the book. These can be independently verified, which provides a modular approach to the verification of software. The text assumes only basic knowledge of standard mathematical concepts that should be familiar to any computer science student. It includes a self-contained introduction to propositional logic and first-order reasoning with theories, followed by a study of program verification that combines theoretical and practical aspects - from a program logic (a variant of Hoare logic for programs containing user-provided annotations) to the use of a realistic tool for the verification of C programs (annotated using the ACSL specification language), through the generation of verification conditions and the static verification of runtime errors.
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