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Page 4866 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
In the paper under review a normal form result is established for the pre- sentations of Church-Rosser languages.  ...  A Church-Rosser language ZL on an alphabet ~ is specified through a Church-Rosser language system.  ... 

Regular Languages Are Church-Rosser Congruential

Volker Diekert, Manfred Kufleitner, Klaus Reinhardt, Tobias Walter
2015 Journal of the ACM  
Padding with u and v yields normal forms v g ∈ A * for g ∈ G : ϕ(v g ) = g , |v g | = |v h | for all g , h ∈ G .  ...  rewriting McNaughton, Narendran, and Otto, JACM 1988 L ⊆ A * is called a Church-Rosser congruential language (CRCL), if there is some finite, confluent and length reducing semi-Thue system S ⊆ A * ×  ... 
doi:10.1145/2808227 fatcat:zrkgyq5irjbephayvlw375ufbe

Regular Languages are Church-Rosser Congruential [article]

Volker Diekert, Manfred Kufleitner, Klaus Reinhardt, Tobias Walter
2012 arXiv   pre-print
A language L is Church-Rosser congruential, if there exists a finite confluent, and length-reducing semi-Thue system S such that L is a finite union of congruence classes modulo S.  ...  This paper proves a long standing conjecture in formal language theory. It shows that all regular languages are Church-Rosser congruential.  ...  In particular, we see that all regular languages are Church-Rosser congruential.  ... 
arXiv:1202.1148v1 fatcat:5gej2a5anfff7b32ve65d2cybi

Thue systems as rewriting systems

Ronald V. Book
1987 Journal of symbolic computation  
This paper is a survey of recent results on Thue systems, where the systems are viewed as rewriting systems on strings over a finite alphabet.  ...  The emphasis is on Thue systems with the Chureh-Rosser property, where the notion of reduction is based on length-decreasing rewriting rules.  ...  Otto (personal communication) have shown that any group with a finite Church-Rosser presentation is a context-free group.  ... 
doi:10.1016/s0747-7171(87)80021-4 fatcat:pqx6qbrwmngcdfsj6mabwfrxce

Page 2227 of Mathematical Reviews Vol. , Issue 91D [page]

1991 Mathematical Reviews  
For context-free Church-Rosser Thue systems a polynomial time-bound is still obtained, while for finite Church- Rosser Thue systems the time-bound improves to O(|A| x |7}).  ...  The Thue system T is called Church-Rosser if, for all x,y € A*, x +} y implies that x -} z and y -} z for some z € A’*.  ... 

Commutativity in groups presented by finite Church-Rosser Thue systems

Klaus Madlener, Friedrich Otto
1988 RAIRO - Theoretical Informatics and Applications  
A Thue System T on S induces a congruence relation <-> on normal form for each of its congruence classes, and any word can be reduced in linear time to the normal form in its class [5] , Hence, it is  ...  In what follows we are interested in languages of the form A*( {w}*) H IRR (7) , where u is an element of infinité order, and Tis a finite Church-Rosser Thue system presenting a group.  ...  Thus, Corollary 3. 6 implies that the Greendlinger group G cannot be presented by a finite Church-Rosser Thue system. • This last example answers a question raised in [21] .  ... 
doi:10.1051/ita/1988220100931 fatcat:m2j7f3y6cjaw5myj3ylmuqgmwy

Regular Languages Are Church-Rosser Congruential [chapter]

Volker Diekert, Manfred Kufleitner, Klaus Reinhardt, Tobias Walter
2012 Lecture Notes in Computer Science  
In [Niemann and Otto 2005] Church-Rosser languages were characterized as deterministic growing context-sensitive languages. For more results about Church-Rosser languages see e.g.  ...  It was known that there are deterministic linear context-free languages which are not Church-Rosser congruential, but the conjecture was that all regular languages are of this form.  ...  ACKNOWLEDGMENT We thank the anonymous referees for various helpful suggestions which significantly improved the presentation.  ... 
doi:10.1007/978-3-642-31585-5_19 fatcat:42x3d3j6h5gy7ojsei7jbogqju

Parikh-reducing Church-Rosser representations for some classes of regular languages [article]

Tobias Walter
2017 arXiv   pre-print
In this paper the concept of Parikh-reducing Church-Rosser systems is studied.  ...  It is shown that for two classes of regular languages there exist such systems which describe the languages using finitely many equivalence classes of the rewriting system.  ...  A language is Church-Rosser congruential if it is a finite union of equivalence classes of a finite length-reducing Church-Rosser rewriting system.  ... 
arXiv:1703.10056v1 fatcat:sbd6rf3jrbfpxjwemqjfkiio6y

Page 509 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
This paper presents a cubic-time recognition and parsing algo- rithm for conjunctive grammars. Previously such an algorithm was known to exist only for conjunctive grammars in a certain normal form.  ...  Mach. 35 (1988), no. 2, 324-344; MR 89e:68068] intro- duced the class CRCL of Church-Rosser congruential languages as a way to define formal languages by confluent length-reducing string-rewriting systems  ... 

Page 571 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
abstract reduction systems that are not Church-Rosser.  ...  to Chomsky’s normal form, and another normal form for a subclass of linear conjunctive grammars.  ... 

Term-rewriting implementation of equational logic programming [chapter]

Michael J. O'Donnell
1987 Lecture Notes in Computer Science  
Such a view leads to the following schema for Logic Programming. A program is a set of assertions in some logical language.  ...  I n t r o d u c t i o n The most common approach to providing semantics for programming languages is to regard a program as the definition of a collection of functions.  ...  The full Church-Rosser property applies also to many-step reductions. The local Chureh-Rosser property implies the full Church-Rosser property only for terminating systems.  ... 
doi:10.1007/3-540-17220-3_1 fatcat:xq7v3m2nmzdb3cjh7bdygcv4ze

Elements of Finite Order for Finite Monadic Church-Rosser Thue Systems

Friedrich Otto
1985 Transactions of the American Mathematical Society  
Thue systems that satisfy the Church-Rosser property [3, 4, 9] are of special interest, since a finite Church-Rosser Thue system defines a unique normal form for each of its congruence classes, and any  ...  word can be reduced in linear time to the normal form of its class [4] .  ...  In particular, for a finite, monadic, Church-Rosser Thue system, the word problem is decidable in linear time [4] . 2. Idempotents for special Church-Rosser TIlUe systems.  ... 
doi:10.2307/2000102 fatcat:5xkuy525l5ar5isytdtvzn4ghy

The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages [chapter]

Gundula Niemann, Friedrich Otto
1998 Lecture Notes in Computer Science  
and the Church-Rosser languages, respectively.  ...  The growing context-sensitive languages have been classified through the shrinking two-pushdown automaton, the deterministic version of which characterizes the class of generalized Church-Rosser languages  ...  Acknowledgments We gratefully acknowledge the detailed comments of two anonymous referees that led to a remarkable simplification of the structure of the paper.  ... 
doi:10.1007/bfb0053554 fatcat:wuip36fa7vgnzl6rbki7pacdle

The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages

Gundula Niemann, Friedrich Otto
2005 Information and Computation  
and the Church-Rosser languages, respectively.  ...  The growing context-sensitive languages have been classified through the shrinking two-pushdown automaton, the deterministic version of which characterizes the class of generalized Church-Rosser languages  ...  Acknowledgments We gratefully acknowledge the detailed comments of two anonymous referees that led to a remarkable simplification of the structure of the paper.  ... 
doi:10.1016/j.ic.2004.09.003 fatcat:t4f3hgckcjcnxj64dns2mjzoji

Page 20 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
The author in this note explains Jantzen’s example by proving that if a Thue system of the form {(w,e)} is not Church- Rosser then there is no Church- Rosser Thue system equivalent to it. John P.  ...  If a Thue system is not Church- Rosser, there still may be some Church - Rosser system which generates the same Thue congruence.  ... 
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