Get BOOK. Bradley Author : Aaron R. The Calculus of Computation. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories.
This textbook also presents a logical approach to engineering correct software. The increasing ubiquity of computers makes implementing correct systems more important than ever. Verification exercises develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems.
For readers interested in learning more about computational logic, decision procedures, verification, and other areas of formal methods, the final chapter outlines courses of further study. Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available.
Induction provides the mathematical basis for analyzing program correctness. Chapter 5 turns to the primary motivating application of computational logic compktation this book, the task of verifying programs.
First, they are sometimes decidable when the full theory is not see Chapters 9, 10, and Second, they are sometimes e ciently decidable when the full theory is not compare Chapters 7 and 8. Chapters 9 and 11 turn to decision procedures for non-arithmetical theories. Chapter 9 discusses the classic congruence closure algorithm for equality with uninterpreted functions and extends it to reason about data structures like lists, trees, and arrays.
Chapter 11 presents decision procedures for larger fragments of theories that formalize array-like data structures. Decision procedures are most useful when they are combined. The decision procedures of Chapters 8, 9, and 11 are all combinable using the Nelson-Oppen method. Chapter 12 presents a methodology for constructing invariant generation procedures.
These procedures reason inductively about programs to aid in. For now, developing manma static analysis is one of the easiest ways of bringing formal methods into general usage, as a typical static analysis requires little or no input from the programmer. Tye chapter presents a general methodology and two instances of the method for deducing arithmetical properties of programs. This book can be used in various ways and taught at multiple levels. There are two main tracks: We have annotated several sections with a to indicate that they provide additional depth that is unnecessary for understanding subsequent computatoon.
Additionally, all proofs may be skipped without preventing a general understanding of the material. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations.
This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering.
This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations. Mathematics of Computation. Get Books. Mathematics and Computation in Music. The 24 revised full papers presented and the 12 short papers were carefully reviewed and selected from 62 submissions.
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