Ebook: Combinatorial Algorithms on Words

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 interest­ 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 sin­ gle reference. It should be clear that the book's emphasis is on aspects of combinatorics and com­ 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 auto­ mata and formal languages, we have allocated very little space to them.

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Content:
Front Matter....Pages I-VIII
Open Problems in Stringology....Pages 1-8
Front Matter....Pages 9-9
Efficient String Matching with Don’t-Care Patterns....Pages 11-29
Optimal Factor Transducers....Pages 31-43
Relating the Average-Case Costs of the Brute-Force and Knuth-Morris-Pratt String Matching Algorithm....Pages 45-58
Algorithms for Factorizing and Testing Subsemigroups....Pages 59-81
Front Matter....Pages 83-83
The Myriad Virtues of Subword Trees....Pages 85-96
Efficient and Elegant Subword-Tree Construction....Pages 97-107
Front Matter....Pages 109-109
Textual Substitution Techniques for Data Compression....Pages 111-129
Variations on a theme by Ziv and Lempel....Pages 131-140
Compression of Two-Dimensional Images....Pages 141-154
Optimal Parsing of Strings....Pages 155-167
Novel Compression of Sparse Bit-Strings — Preliminary Report....Pages 169-183
Front Matter....Pages 185-185
The Use and Usefulness of Numeration Systems....Pages 187-203
Enumeration of Strings....Pages 205-228
Two counting problems solved via string encodings....Pages 229-240
Some Uses of the Mellin Integral Transform in the Analysis of Algorithms....Pages 241-254
Front Matter....Pages 255-255
Periodicities in Strings....Pages 257-269
Linear Time Recognition of Squarefree Strings....Pages 271-278
Discovering Repetitions in Strings....Pages 279-288
Some Decision Results on Nonrepetitive Words....Pages 289-295
Front Matter....Pages 297-297
On the Complexity of Some Word Problems That Arise in Testing the Security of Protocols....Pages 299-314
Code Properties and Derivatives of DOL Systems....Pages 315-327
Words over a Partially Commutative Alphabet....Pages 329-340
The Complexity of Two-Way Pushdown Automata and Recursive Programs....Pages 341-356
Context-Free Grammars and Random Number Generation....Pages 357-361
Back Matter....Pages 363-363

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Content:
Front Matter....Pages I-VIII
Open Problems in Stringology....Pages 1-8
Front Matter....Pages 9-9
Efficient String Matching with Don’t-Care Patterns....Pages 11-29
Optimal Factor Transducers....Pages 31-43
Relating the Average-Case Costs of the Brute-Force and Knuth-Morris-Pratt String Matching Algorithm....Pages 45-58
Algorithms for Factorizing and Testing Subsemigroups....Pages 59-81
Front Matter....Pages 83-83
The Myriad Virtues of Subword Trees....Pages 85-96
Efficient and Elegant Subword-Tree Construction....Pages 97-107
Front Matter....Pages 109-109
Textual Substitution Techniques for Data Compression....Pages 111-129
Variations on a theme by Ziv and Lempel....Pages 131-140
Compression of Two-Dimensional Images....Pages 141-154
Optimal Parsing of Strings....Pages 155-167
Novel Compression of Sparse Bit-Strings — Preliminary Report....Pages 169-183
Front Matter....Pages 185-185
The Use and Usefulness of Numeration Systems....Pages 187-203
Enumeration of Strings....Pages 205-228
Two counting problems solved via string encodings....Pages 229-240
Some Uses of the Mellin Integral Transform in the Analysis of Algorithms....Pages 241-254
Front Matter....Pages 255-255
Periodicities in Strings....Pages 257-269
Linear Time Recognition of Squarefree Strings....Pages 271-278
Discovering Repetitions in Strings....Pages 279-288
Some Decision Results on Nonrepetitive Words....Pages 289-295
Front Matter....Pages 297-297
On the Complexity of Some Word Problems That Arise in Testing the Security of Protocols....Pages 299-314
Code Properties and Derivatives of DOL Systems....Pages 315-327
Words over a Partially Commutative Alphabet....Pages 329-340
The Complexity of Two-Way Pushdown Automata and Recursive Programs....Pages 341-356
Context-Free Grammars and Random Number Generation....Pages 357-361
Back Matter....Pages 363-363
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