The Stanford PASCAL verifier is an interactive program verification system. It automates much of ... more The Stanford PASCAL verifier is an interactive program verification system. It automates much of the work necessary to analyze a program for consistency with its documentation, and to give a rigorous mathematical proof of such consistency or to pin-point areas of inconsistency. It has been shown to have applications as an aid to programming, and to have potential for development as a new and useful tool in the production of reliable software.
The combination of two of the twentieth centurys most influential and revolutionary scientific th... more The combination of two of the twentieth centurys most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book. The text covers the basic building blocks of quantum information processing, quantum bits and quantum gates, showing their relationship to the key quantum concepts of quantum measurement, quantum state transformation, and entanglement between quantum subsystems; it treats quantum algorithms, discussing notions of complexity and describing a number of simple algorithms as well as the most significant algorithms to date; and it explores entanglement and robust quantum computation, investigating such topics as quantifying entanglement, decoherence, quantum error correction, and fault tolerance.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
A method of documenting exception propagation and handling in Ada programs is proposed. Exception... more A method of documenting exception propagation and handling in Ada programs is proposed. Exception propagation declarations are introduced as a new component of Ada specifications. This permits documentation of those exceptions that can be propagated by a subprogram. Exception handlers are documented by entry assertions. Axioms and proof rules for Ada exceptions are given. These rules are simple extensions of previous rules for Pascal and define an axiomatic semantics of Ada exceptions. As a result, Ada programs specified according to the method can be analysed by formal proof techniques for consistency with their specifications, even if they employ exception propagation and handling to achieve required results (i.e. non-error situations). Example verifications are given.
2000 Ieee International Conference on Multimedia and Expo Icme2000 Proceedings Latest Advances in the Fast Changing World of Multimedia, Feb 1, 2000
We describe a genetic segmentation algorithm for video. This algorithm operates on segments of a ... more We describe a genetic segmentation algorithm for video. This algorithm operates on segments of a string representation. It is similar to both classical genetic algorithms that operate on bits of a string and genetic grouping algorithms that operate on subsets of a set. For evaluating segmentations, we define similarity adjacency functions, which are extremely expensive to optimize with traditional methods. The evolutionary nature of genetic algorithms offers a further advantage by enabling incremental segmentation. Applications include video summarization and indexing for browsing, plus adapting to user access patterns.
The Stanford PASCAL verifier is an interactive program verification system. It automates much of ... more The Stanford PASCAL verifier is an interactive program verification system. It automates much of the work necessary to analyze a program for consistency with its documentation, and to give a rigorous mathematical proof of such consistency or to pin-point areas of inconsistency. It has been shown to have applications as an aid to programming, and to have potential for development as a new and useful tool in the production of reliable software.
The combination of two of the twentieth centurys most influential and revolutionary scientific th... more The combination of two of the twentieth centurys most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book. The text covers the basic building blocks of quantum information processing, quantum bits and quantum gates, showing their relationship to the key quantum concepts of quantum measurement, quantum state transformation, and entanglement between quantum subsystems; it treats quantum algorithms, discussing notions of complexity and describing a number of simple algorithms as well as the most significant algorithms to date; and it explores entanglement and robust quantum computation, investigating such topics as quantifying entanglement, decoherence, quantum error correction, and fault tolerance.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
We present efficient implementations of a number of operations for quantum computers. These inclu... more We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of the phase adjustments to block matrix transformations. These operations generalize those used in proposed quantum search algorithms.
A method of documenting exception propagation and handling in Ada programs is proposed. Exception... more A method of documenting exception propagation and handling in Ada programs is proposed. Exception propagation declarations are introduced as a new component of Ada specifications. This permits documentation of those exceptions that can be propagated by a subprogram. Exception handlers are documented by entry assertions. Axioms and proof rules for Ada exceptions are given. These rules are simple extensions of previous rules for Pascal and define an axiomatic semantics of Ada exceptions. As a result, Ada programs specified according to the method can be analysed by formal proof techniques for consistency with their specifications, even if they employ exception propagation and handling to achieve required results (i.e. non-error situations). Example verifications are given.
2000 Ieee International Conference on Multimedia and Expo Icme2000 Proceedings Latest Advances in the Fast Changing World of Multimedia, Feb 1, 2000
We describe a genetic segmentation algorithm for video. This algorithm operates on segments of a ... more We describe a genetic segmentation algorithm for video. This algorithm operates on segments of a string representation. It is similar to both classical genetic algorithms that operate on bits of a string and genetic grouping algorithms that operate on subsets of a set. For evaluating segmentations, we define similarity adjacency functions, which are extremely expensive to optimize with traditional methods. The evolutionary nature of genetic algorithms offers a further advantage by enabling incremental segmentation. Applications include video summarization and indexing for browsing, plus adapting to user access patterns.
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Papers by Wolfgang Polak