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Difference between revisions of "Scattered Context Grammars research"
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   authors    = S. Greibach, J. Hopcroft |
 
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== Results ==
 
== Results ==
  
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==== Normal Forms of Propagating Scattered Context Grammars ====
 
==== Normal Forms of Propagating Scattered Context Grammars ====
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   authors    = S. Greibach, J. Hopcroft |
 
   authors    = S. Greibach, J. Hopcroft |
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==== Closure Properties of Propagating Scattered Context Grammars ====
 
==== Closure Properties of Propagating Scattered Context Grammars ====
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   authors    = S. Greibach, J. Hopcroft |
 
   authors    = S. Greibach, J. Hopcroft |
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==== Extended Propagating Scattered Context Grammars ====
 
==== Extended Propagating Scattered Context Grammars ====
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'''Based on'''
 
'''Based on'''
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   authors    = J. Gonczarowski, M. K. Warmuth |
 
   authors    = J. Gonczarowski, M. K. Warmuth |
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==== Propagating Scattered Context Grammars Using Leftmost Derivations ====
 
==== Propagating Scattered Context Grammars Using Leftmost Derivations ====
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'''Based on'''
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{{cite |  
 
   authors    = V. Virkkunen |  
 
   authors    = V. Virkkunen |  
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==== Power of Scattered Context Grammars ====
 
==== Power of Scattered Context Grammars ====
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'''Based on'''
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{{cite |  
 
   authors    = V. Virkkunen |  
 
   authors    = V. Virkkunen |  
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==== Reduction of Scattered Context Grammars ====
 
==== Reduction of Scattered Context Grammars ====
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'''Based on'''
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{{cite |  
 
   authors = A. Meduna|
 
   authors = A. Meduna|
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   url      = http://missing.pdf
 
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=== Own Research ===
 
=== Own Research ===
  
 
==== Generation of Sentences with Their Parses ====
 
==== Generation of Sentences with Their Parses ====
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'''Based on'''
 
'''Based on'''
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{{cite |  
 
{{cite |  
 
   authors = A. Meduna, J. Techet|
 
   authors = A. Meduna, J. Techet|
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==== k-Limited Erasing ====
 
==== k-Limited Erasing ====
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'''Based on'''
 
'''Based on'''
  
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==== Scattered Context Grammars with Non-Context-Free Components ====
 
==== Scattered Context Grammars with Non-Context-Free Components ====
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==== Maximal and Minimal Rewriting ====
  
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==== Maximal and Minimal Rewriting ====
 
 
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'''Based on'''
  
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==== n-Limited Derivations ====
 
==== n-Limited Derivations ====
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== Related Literature ==
 
== Related Literature ==
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[[User:Jiri|Jiri]] 11:06, 26 November 2007 (CET)
 
[[User:Jiri|Jiri]] 11:06, 26 November 2007 (CET)

Revision as of 12:56, 26 November 2007

!!! WORK IN PROGRESS - Please do not read :-) !!!

Introduction

Scattered context grammars were introduced by S. Greibach and J. Hopcroft in 1969 as a straightforward generalization of context-free grammars. Each production of these grammars contains n context-free productions which are applied in parallel to the current sentential form. For example a scattered context production

(A, B, C) \rightarrow (a, b, c)

which consists of three context-free productions,

A \rightarrow aA, B \rightarrow bB, C \rightarrow cC,

is applicable to the sentential form aAbBcC, so

aAbBcC \Rightarrow aaAbbBccC.

It is easy to see that by adding productions

S \rightarrow ABC

and

(A, B, C) \rightarrow (a, b, c),

where S is the start symbol of the grammar, we can easily describe the non-context-free language

\{a^nb^nc^n : n \geq 1 \}.

The first advantage of scattered context grammars can be seen here - by using several context-free productions in parallel, we are able to describe some context-sensitive languages. Furthermore, by only extending context-free grammars, which are well studied and used in many practical applications, we preserve the simplicity of language description. In addition, for modeling context dependencies which span over the whole sentential form (for example in the above example), the description is much simpler than when using context-sensitive grammars.

Basic Definitions

Formal Languages

The reader is expected to be familiar with the basics of formal language theory. This section is meant to describe the used terminology rather than to explain the basics of formal language theory.

References

(pdf) A. Meduna. Automata and Languages: Theory and Applications. Springer, 2000, pp. 920.

(pdf) G. Rozenberg and A. Salomaa. Handbook of Formal Languages. Springer, 1997, pp. 2051.

(pdf) A. Salomaa. Formal Languages. Academic Press, 1973, pp. 322.

Scattered Context Grammars

References

(pdf) S. Greibach, J. Hopcroft. Scattered Context Grammars. Journal of Computer and System Sciences, 1969, pp. 233-247.

Results

Known Results

Normal Forms of Propagating Scattered Context Grammars

Based on

(pdf) S. Greibach, J. Hopcroft. Scattered Context Grammars. Journal of Computer and System Sciences, 1969, pp. 233-247.

Closure Properties of Propagating Scattered Context Grammars

Based on

(pdf) S. Greibach, J. Hopcroft. Scattered Context Grammars. Journal of Computer and System Sciences, 1969, pp. 233-247.

Extended Propagating Scattered Context Grammars

Based on

(pdf) J. Gonczarowski, M. K. Warmuth. Scattered Versus Context-Sensitive Rewriting. Acta Informatica, 1989, pp. 81-95.

Propagating Scattered Context Grammars Using Leftmost Derivations

Based on

(pdf) V. Virkkunen. On Scattered Context Grammars. Acta Universitatis Ouluensis, 1973, pp. 75-82.

Power of Scattered Context Grammars

Based on

(pdf) V. Virkkunen. On Scattered Context Grammars. Acta Universitatis Ouluensis, 1973, pp. 75-82.

Reduction of Scattered Context Grammars

Based on

(pdf) A. Meduna. Economical Transformations of Scattered Context Grammars to Phrase-Structure Grammars. Acta Cybernetica, 1998, pp. 225-242.

(pdf) A. Meduna. Generative Power of Three-Nonterminal Scattered Context Grammars. Theoretical Computer Science, 2000, pp. 625-631.

(pdf) G. Vaszil. On the Descriptional Complexity of Some Rewriting Mechanisms Regulated by Context Conditions. Theoretical Computer Science, 2005, pp. 361-373.

Own Research

Generation of Sentences with Their Parses

Based on

(pdf) A. Meduna, J. Techet. Generation of Sentences with Their Parses: the Case of Propagating Scattered Context Grammars. Acta Cybernetica, 2005, pp. 11-20.

(pdf) A. Meduna, J. Techet. Canonical Scattered Context Generators of Sentences with Their Parses (to appear). Theoretical Computer Science, 2007/8, pp. ???-???.

(pdf) J. Techet. Scattered Context Generators of Sentences with Their Parses. Pre-proceedings of the 1st Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, 2005, pp. 68-77.

(pdf) A. Meduna, J. Techet. Reduction of Scattered Context Generators of Sentences Preceded by Their Leftmost Parses. Proceedings of 9th International Workshop on Descriptional Complexity of Formal Systems, 2007, pp. 178-185.

References

(pdf) V. Geffert. Context-Free-Like Forms for the Phrase-Structure Grammars. Proceedings of the Mathematical Foundations of Computer Science 1988, 1988, pp. 309-317.

(pdf) H. C. M. Kleijn and G. Rozenberg. On the Generative Power of Regular Pattern Grammars. Acta Informatica, 1983, pp. 391-411.

k-Limited Erasing

Based on

(pdf) J. Techet. k-Limited Erasing Performed by Scattered Context Grammars. Proceedings of the 2nd International Workshop on Formal Models WFM '07, 2007, pp. 227-234.

Scattered Context Grammars with Non-Context-Free Components

Based on

(pdf) J. Techet. A Note on Scattered Context Grammars with Non-Context-Free Components. MEMICS 2007 Proceedings, 2007, pp. 225-232.

References

(pdf) O. Ibarra. Simple Matrix Languages. Information and Control, 1970, pp. 359-394.

(pdf) G. Paun. Linear Simple Matrix Languages. Elektronische Informationsverarbeitung und Kybernetik, 1978, pp. 377-384.

Maximal and Minimal Rewriting

Based on

(pdf) A. Meduna, J. Techet. Maximal and Minimal Scattered Context Rewriting. FCT 2007 Proceedings, 2007, pp. 412-423.

References

(pdf) Takumi Kasai. An Hierarchy Between Context-Free and Context-Sensitive Languages. Journal of Computer and System Sciences, 1970, pp. 492-508.

n-Limited Derivations

References

(pdf) Takumi Kasai. An Hierarchy Between Context-Free and Context-Sensitive Languages. Journal of Computer and System Sciences, 1970, pp. 492-508.

Related Literature

(pdf) H. Fernau. Scattered Context Grammars with Regulation. Annals of Bucharest University, Mathematics-Informatics Series, 1996, pp. 41-49.

(pdf) D. Milgram, A Rosenfeld. A Note on Scattered Context Grammars. Information Processing Letters, 1971, pp. 47-50.

(pdf) Armin B. Cremers. Normal Forms for Context-Sensitive Grammars. Acta Informatica, 1973, pp. 59-73.

(pdf) J. Techet. Částečně paralelní generování jazyků. Faculty of Information Technology BUT, 2005, pp. 55.

Jiri 11:06, 26 November 2007 (CET)

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