Context-free languages and primitive words:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
World Scientific
2015
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 506 S. |
| ISBN: | 9789814271660 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804150558285627392 |
|---|---|
| adam_text | Contents
Pre f ace
vii
1.
Preliminaries
1
1.1
Background
.......................... 1
1.2
Bibliographical Remarks
................... 24
2.
Combinatorial Properties of Words and Languages
27
2.1
Words
............................. 27
2.2
Languages
........................... 44
2.3
Decidability
.......................... 76
2.4
Bibliographical Remarks
................... 77
3.
Rewriting Systems
83
3.1
Basic Definitions of Rewriting Systems and Related Topics
83
3.2
Bibliographical Remarks
................... 87
4.
Iteration Lemmata
89
4.1
Iteration Lemma for Regular and Linear Languages
.... 89
4.2
Bar-Hillel Lemma, Ogden Lemma,
Bader-
Moura
Lemma
. 92
4.3 Dömösi-Ito-Katsura-Nehaniv
Lemma
............ 98
4.4
Wise Lemma
......................... 99
4.5
Bibliographical Remarks
................... 101
5.
Other Characterizations of Context-Free Languages
103
5.1
Sequential Transducer and General Sequential Mappings
. 103
5.2
Context-Free Languages and Pushdown Automata
.... 106
IX
x
Context-Free Languages and Primitive Words
5.3
Deterministic Pushdown Automaton
............ 112
5.4
Chomsky-Schiitzenberger-Stanley Type Characterizations
120
5.5
Interchange Lemma
...................... 123
5.6
Parikh s Theorem
....................... 126
5.7
Context-Flee Languages and Ultimately Periodic Sets of
Positive Integers
....................... 130
5.8
Bibliographical Remarks
................... 133
6.
Bounded and Palindromic Languages
135
6.1
Bounded Regular and Context-Free Languages
...... 135
6.2
Polyslender Regular and Context-Free Languages
..... 140
6.3
Slender Regular and Context-Free Languages
....... 161
6.4
Polyslender Languages and Trajectories
.......... 168
6.5
Palindromic Regular and Context-Free Languages
..... 171
6.6
Bibliographical Remarks
................... 180
7.
Further Combinatorial Investigations on Primitive Words
183
7.1
Unique Factorizations of Primitive Words
......... 183
7.2
The Value of Primitive Words
................ 194
7.3
Word Insertions and
Primitivity
............... 196
7.4
Robustness
.......................... 211
7.5
Primitive Partial Words
................... 215
7.6
Generalized Periodicity, Generalized
Primitivity, Primitiv¬
ity
Distance of Words
.................... 226
7.7
Bibliographical Remarks
................... 237
8.
Some Properties of the Language of Primitive Words
239
8.1
Iteration Properties
...................... 239
8.2
Ambiguity of Context-free Grammars
............ 241
8.3
Ambiguity of
Q
........................ 245
8.4
Strong Interchangeability
.................. 248
8.5
Primitive Words and Ultimately Periodic Sets of Positive
Integers
............................ 251
8.6
Nonlinearity
.......................... 251
8.7
Square-Free Words of Arbitrary Length
.......... 253
8.8
Rewriting Systems and Primitive Words
.......... 256
8.9
Bibliographical Remarks
................... 265
9.
Primitive Words in Languages
267
Contents
xi
9.1
Lyndon Words
........................ 267
9.2
The Language p+q+
..................... 268
9.3
The Languages Qn,n
> 2.................. 270
9.4
Primitive Words and Dense Languages
........... 272
9.5
Some Operations Preserving
Primitivity
of Words
..... 273
9.6
The Language of Abelian Primitive Words
......... 287
9.7
Pseudo-Primitivity
...................... 297
9.8
The Language of Permutation-Resistant Primitive Words
306
9.9
Bibliographical Remarks
................... 307
10.
Kászonyi-Katsura
Theory
309
10.1
DLI
Languages
........................ 309
10.2
Boxes and Differences
.................... 320
10.3
The Language
Q
Π
(ab*)71
with Some Restrictions on the
Prime Divisors of
η
...................... 323
10.4
Semiboxes
.......................... 327
10.5
The Language
Q
П
(ab*)n with Two Prime Divisors
of
n
.............................. 330
10.6
The Language
Q
Π
(ab*)*1
with Three Prime Divisors
of
η
.............................. 332
10.7
Some Non-Context-Free and
Context-Pree
Languages
. . . 339
10.8
Primitive Words and Disjunctive Languages
........ 340
10.9
Bibliographical Remarks
................... 341
11.
Deri vat ing Primitive Words
343
11.1
Morphisms and
Primitivity
................. 343
11.2
Automata Accepting Primitive Words
........... 352
11.3
Slender Languages Consisting of Primitive Words
..... 356
11.4
Small Context-Free Grammars Generating Primitive Words
360
11.5
Bibliographical Remarks
................... 367
12.
Decidability. Roots, Multisets
371
12.1
Decidability and Undecidability
............... 371
12.2
Roots and Degrees
...................... 381
12.3
Degrees and generalized degrees
............... 384
12.4
Complexity Considerations
.................. 386
12.5
Primitive Multisets
...................... 402
12.6
Bibliographical Remarks
................... 411
xii
Context-
Free Languages and Primitive Words
13.
Context-Free Languages and Non-primitive Words
413
13.1
Non-primitive Words and the
Bar-Hiłlel
Lemma
...... 413
13.2
Context-Free Languages Consisting of Non-primitive Words
413
13.3
Bibliographical Remarks
................... 420
14.
Primitive Words and Palindromes
423
14.1
Primitive Palindromes Are Not Context-Free
....... 423
14.2
Primitive and Minimal Palindromes
............. 427
14.3
Non-Primitive Palindromes in Context-Free Languages
. . 429
14.4
fc-
Palindromes
......................... 431
14.5
Bibliographical Remarks
................... 435
15.
Marcus Contextual Grammars and Primitive Words
437
15.1
Some Results on Nonprimitivity and
Primitivity
Related
to Marcus Contextual Grammars
.............. 437
15.2
Generalizations, Open Problems
............... 446
15.3
Bibliographical Remarks
................... 448
16.
Appendix
1 451
16-1
Turing Machines,
Godei
Numbering, and the Post Corre¬
spondence Problem
...................... 451
16.2
Bibliographical Remarks
................... 461
17.
Appendix
2 463
17.1
Mathematical Background
.................. 463
17.2
Bibliographical Remarks
................... 468
18.
Appendix
3 469
18.1
C^+
Program to Define All Maximal Sceletons with
3
Non¬
terminals up to Symmetries
................. 469
18.2
Bibliographical Remarks
................... 480
Bibliography
481
Index
499
Context-Free Languages
and Primitive Words
A word is said to be primitive if it cannot be
represented as any power of another word. It is
a well-known conjecture that the set of all
primitive words
Q
over a non-trivial alphabet is
not context-free: this conjecture is still open. In
this book, the authors deal with properties of
primitive words over a non-trival alphabet, the
language consisting of all primitive words and
related languages. Moreover, some decidable
and undecidabie problems with respect to the
above languages are discussed as well. As
another try, a search for a non-phrase structure
grammar which generates
Q
is performed.
|
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| language | English |
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| physical | XII, 506 S. |
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| spelling | Dömösi, Pál 1943- Verfasser (DE-588)1064640575 aut Context-free languages and primitive words Pál Dömösi ; Masami Ito Singapore World Scientific 2015 XII, 506 S. txt rdacontent n rdamedia nc rdacarrier Kontextfreie Sprache (DE-588)4165150-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Kontextfreie Sprache (DE-588)4165150-9 s Itō, Masami 1941- Verfasser (DE-588)124830986 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026130037&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026130037&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Dömösi, Pál 1943- Itō, Masami 1941- Context-free languages and primitive words Kontextfreie Sprache (DE-588)4165150-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4165150-9 (DE-588)4037951-6 |
| title | Context-free languages and primitive words |
| title_auth | Context-free languages and primitive words |
| title_exact_search | Context-free languages and primitive words |
| title_full | Context-free languages and primitive words Pál Dömösi ; Masami Ito |
| title_fullStr | Context-free languages and primitive words Pál Dömösi ; Masami Ito |
| title_full_unstemmed | Context-free languages and primitive words Pál Dömösi ; Masami Ito |
| title_short | Context-free languages and primitive words |
| title_sort | context free languages and primitive words |
| topic | Kontextfreie Sprache (DE-588)4165150-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Kontextfreie Sprache Mathematische Logik |
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