A Complete Characterization Of Termination Of 0 Superscript P 1 Superscript Q 1 Superscript R 0 Superscript S
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A Complete Characterization of Termination of 0[superscript P] 1[superscript Q] -> 1[superscript R] 0[superscript S]
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Abstract: "We completely characterize termination of one-rule string rewriting systems of the form 0[superscript p] 1[superscript q] -> 1[superscript r] 0[superscript s] for every choice of positive integers p, q, r, and s. For the simply terminating cases, we give a sharp estimate of the complexity of derivation lengths."
Analytical Methods of Optimization
Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. It takes the approach most appropriate for applications to problems of optimizing the behavior of engineering systems. Two of these problem areas have strongly influenced this presentation: the design of the control systems and the choice of rocket trajectories to be followed by terrestrial and extraterrestrial vehicles. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Prerequisites include a course in the analysis of functions of many real variables and a familiarity with the elementary theory of ordinary differential equations, especially linear equations. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. Solutions to the exercises are available from the publisher upon request.
Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.