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This book treats the problem of formulating models in mathematical programming, and thereafter solving the resulting model. Particular emphasis is placed on the interaction between the two. The topic is viewed from different angles, namely linear programming (Walter Murray), integer programming (Ellis Johnson), network flows (John Mulvey), and stochastic programming (Roger J-B Wets). The book will be very useful for any mathematics programmer or operations researcher who works in the field of real-world modelling. The book is an important part of any university course in modelling, particularly in operations research, economics and business. The book also contains an article on the origins of mathematical programming (Alexander Rinnooy Kan). This is important reading for anyone interested in the history of the field.
Introduction. Regular syntaxes. Definitions on regular syntaxes and expressions. Finite-state acceptors. The finite-state (FS) acceptor. The 1-predictive finite-state (1-FS) acceptor. The 1-predictive finite-state (1-FS) acceptor program. Generation of finite-state acceptors. The generation scheme for 1-FS acceptors. The definitions of follow and dirsymb. The generation scheme for 1-FS acceptor programs. Regular translation syntaxes. Examples of regular translation syntaxes. The generalized regular translation syntax. Finite-state transducers. The 1-predictive finite-state (1-FS) transducer. The 1-predictive finite-state transducer program. The generalized 1-predictive finite-state transducer program. Generation of finite-state transducers. Extended contex-free syntaxes. Definitions on extended context-free syntaxes and expressions. Symple examples of extended context-free syntaxes. Relation between context-free and extended context-free syntax. Alternative definitions. Pushdown acceptors. Generation of pushdown acceptors. Extended context-free translation syntaxes. Pushdown transducers. Generation of pushdown transducers. Attributed syntaxes. Attributed pushdown transducers and their generation. Appendix 1. Appendix 2. References.