Combinatorial Algorithms on Words refers to the collection of manipulations of strings of symbols (words) - not necessarily from a finite alphabet - that exploit the combinatorial properties of the logical/physical input arrangement to achieve efficient computational performances. The model of computation may be any of the established serial paradigms (e.g. RAM's, Turing Machines), or one of the emerging parallel models (e.g. PRAM ,WRAM, Systolic Arrays, CCC). This book focuses on some of the accomplishments of recent years in such disparate areas as pattern matching, data compression, free groups, coding theory, parallel and VLSI computation, and symbolic dynamics; these share a common flavor, yet ltave not been examined together in the past. In addition to being theoretically interestยญ ing, these studies have had significant applications. It happens that these works have all too frequently been carried out in isolation, with contributions addressing similar issues scattered throughout a rather diverse body of literature. We felt that it would be advantageous to both current and future researchers to collect this work in a sinยญ gle reference. It should be clear that the book's emphasis is on aspects of combinatorics and comยญ plexity rather than logic, foundations, and decidability. In view of the large body of research and the degree of unity already achieved by studies in the theory of autoยญ mata and formal languages, we have allocated very little space to them
CONTENT
Open Problems in Stringology -- 1 โ{128}{148} String Matching -- Efficient String Matching with Donโ{128}{153}t-care Patterns -- Optimal Factor Transducers -- Relating the Average-case Cost of the Brute force and the Knuth-Morris-Pratt String Matching Algorithm -- Algorithms for Factorizing and Testing Subsemigroups -- 2 โ{128}{148} Subword Trees -- The Myriad Virtues of Subword Trees -- Efficient and Elegant Subword Tree Construction -- 3 โ{128}{148} Data Compression -- Textual Substitution Techniques for Data Compression -- Variations on a Theme by Ziv and Lempel -- Compression of Two-dimensional Images -- Optimal Parsing of Strings -- Novel Compression of Sparse Bit Strings -- 4 โ{128}{148} Counting -- The Use and Usefulness of Numeration Systems -- Enumeration of Strings -- Two Counting Problems Solved via String Encodings -- Some Uses of the Mellin integral Transform in the Analysis of Algorithms -- 5 โ{128}{148} Periods and Other Regularities -- Periodicities in Strings -- Linear Time Recognition of Square free Strings -- Discovering Repetitions in Strings -- Some Decision Results on Nonrepetitive Words -- 6 โ{128}{148} Miscellaneous -- On the Complexity of some Word Problems Which Arise in Testing the Security of Protocols -- Code Properties and Derivatives of DOL Systems -- Words over a Partially Commutative Alphabet -- The Complexity of Two-way Pushdown Automata and Recursive Programs -- On Context Free Grammars and Random Number Generation
