Filters








1,316 Hits in 4.4 sec

On deciding the confluence of a finite string-rewriting system on a given congruence class

Friedrich Otto
1987 Journal of computer and system sciences (Print)  
A string-rewriting system R on alphabet C induces a congruence ++ 2 on the free monoid 27 generated by Z, and hence, the set M, of congruence classes modulo -2 is a monoid.  ...  In general it is undecidable whether or not a given finite string-rewriting system R is confluent on a given congruence class [w]~, even when only length-reducing systems are considered.  ...  ACKNOWLEDGMENTS The author thanks Professor R. V. Book and Professor K. Madlener for many fruitful discussions regarding the results presented in this paper.  ... 
doi:10.1016/0022-0000(87)90017-1 fatcat:uuahdoiqerd7lmkymitfrgngd4

Page 1649 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
In this paper, the author proves that the word problem is reducible to its restricted version for finite, special string rewriting systems.  ...  Its reflexive, symmetric and transitive closure ++}. is a congruence on A*. The congruence classes form a monoid M(A, T).  ... 

Page 5981 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Finally, the authors present a specialized completion procedure that, given a finite monadic string-rewriting system presenting a group as input, attempts to construct an equivalent monadic system that  ...  R is called weakly confluent if it is confluent on all the congruence classes [a] with a € ZU {e}.  ... 

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.  ...  problem that cannot be presented by any finite complete rewriting system.  ... 
doi:10.1016/s0747-7171(87)80021-4 fatcat:pqx6qbrwmngcdfsj6mabwfrxce

Page 2813 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
This result provides, for a given finite, special string-rewriting system R on an alphabet A such that R is confluent on the congruence class [w]r for some word w in A*, an equivalent finite, special string-rewriting  ...  The authors derive a number of interesting decidability results for finite, special string-rewriting systems that are confluent on some congruence class.  ... 

When is an extension of a specification consistent? Decidable and undecidable cases

Friedrich Otto
1991 Journal of symbolic computation  
Question: Is (E l , El) a consistent extension of (:Z, E)? For the special ease of string-rewriting systems we present decidable and undeeidable eases of this problem.  ...  Given the system R (or E) and the ordering > as input, the Knuth-Bendix completion procedure tries to derive a system R~ such that R and R~ are equivalent, i.e. they both define the congruence ~-on S,  ...  Here we investigate this problem in the special case of string-rewriting systems. Let ~E be a finite alphabet, and R be a finite string-rewriting system on ~;.  ... 
doi:10.1016/s0747-7171(08)80150-2 fatcat:nkdhm6qvg5b4raop56t755nzpu

On weakly confluent monadic string-rewriting systems

K. Madlener, P. Narendran, F. Otto, L. Zhang
1993 Theoretical Computer Science  
Here a monadic string-rewriting system R on some alphabet z is called weakly confluent if it is confluent on all the congruence classes [a]s, with ao,Su {e}.  ...  It is investigated as to how far the various decidability results for finite, monadic, and confluent string-rewriting systems can be carried over to the class of finite monadic string-rewriting systems  ...  This corresponds to the situation of completing a finite special string-rewriting system R on [elR considered by one of the authors in [31] .  ... 
doi:10.1016/0304-3975(93)90213-d fatcat:ba7rvt2rb5fepptcymu4ql6ln4

Monoid presentations of groups by finite special string-rewriting systems

Duncan W. Parkes, V. Yu. Shavrukov, Richard M. Thomas
2004 RAIRO - Theoretical Informatics and Applications  
We show that the class of groups which have monoid presentations by means of finite special [λ]-confluent string-rewriting systems strictly contains the class of plain groups (the groups which are free  ...  products of a finitely generated free group and finitely many finite groups), and that any group which has an infinite cyclic central subgroup can be presented by such a string-rewriting system if and  ...  The referees' helpful comments allowed us to considerably simplify our treatment of Case 2 in the proof of Proposition 4.4.  ... 
doi:10.1051/ita:2004012 fatcat:k7zv4m76zfdnhfbztjs2k7qmga

About the descriptive power of certain classes of finite string-rewriting systems

Klaus Madlener, Friedrich Otto
1989 Theoretical Computer Science  
So the word problem for a monoid presented by a finite canonical string-rewriting system is decidable.  ...  Many decision problems that are undecidable in general can be solved with various degrees of complexity for various classes of finite canonical string-rewriting systems.  ...  Groups presented by finite special string-rewriting systems Let C,, be the class of finite special string-rewriting systems R that are confluent, let C,,,, be the class of finite special string-rewriting  ... 
doi:10.1016/0304-3975(89)90002-9 fatcat:onterhtqvncyxk34zrcszlhmli

Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings

Klaus Madlener, Birgit Reinert
1998 Theoretical Computer Science  
For several classes of finitely presented groups we show explicitly how Grabner basis methods are related to existing solutions of the subgroup problem that are based on rewriting methods.  ...  These characterizations allow to transfer well known results from the theory of string rewriting systems for presenting monoids and groups to the algebraic setting of subalgebras and ideals in monoid and  ...  We both thank Andrea Sattler-Klein, Teo Mora, Paliath Narendran and Friedrich Otto for valuable discussions on parts of this paper.  ... 
doi:10.1016/s0304-3975(98)00077-2 fatcat:j5phzlmmqzeutm2wuviychbloe

Groups presented by certain classes of finite length-reducing string-rewriting systems [chapter]

Klaus Madlener, Friedrich Otto
1987 Lecture Notes in Computer Science  
A string-rewriting system R on I is confluent, if each of its congruence classes contains a unique irreducible word, which can then be taken as the normal form of its class.  ...  Here 1 denotes the empty word, and [w] R denotes the c o n g r u e n c e class of w ~ I* modulo the congruence ~ )R" A s t r i n g -r e w r i t i n g system R on ~ is called length-reducing, if llJ > Irs  ... 
doi:10.1007/3-540-17220-3_12 fatcat:lciybdavdjckdpqztukuiq7efa

Page 3331 of Mathematical Reviews Vol. , Issue 93f [page]

1993 Mathematical Reviews  
The author proves that the problem of deciding whether a finite special string-rewriting system is confluent on a given congruence class is solvable in polynomial time.  ...  finite special string-rewriting systems.  ... 

Some results about confluence on a given congruence class [chapter]

Friedrich Otto
1987 Lecture Notes in Computer Science  
On the other hand, for certain subclasses of these systems confluence on a given congruence class is decidable.  ...  It is undecidable in general whether or not a term-rewriting system is confluent on a given congruence class.  ...  The author wants to thank Ron Book for bringing this problem to his attention, and for many fruitful discussions regarding the various results presented in this paper.  ... 
doi:10.1007/3-540-17220-3_13 fatcat:3lrnrib5zza6vndtefatyh6mii

THE INCLUSION PROBLEM OF CONTEXT-FREE LANGUAGES: SOME TRACTABLE CASES

ALBERTO BERTONI, CHRISTIAN CHOFFRUT, ROBERTO RADICIONI
2011 International Journal of Foundations of Computer Science  
We study the problem of testing whether a context-free language is included in a fixed set L0, where L0 is the language of words reducing to the empty word in the monoid defined by a complete string rewrite  ...  system.  ...  We showed that verifying whether all the words a context-free language are mapped to the empty word in a cancellative monoid can be reduced to testing the equality of two SLPs in the same monoid.  ... 
doi:10.1142/s0129054111008040 fatcat:iqu2fcconbcepmuly67ezyao3u

Page 1104 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
{For the entire collection see MR 95j:03003.} 96b:68094 68Q42 Otto, Friedrich (D-KSSL-MI; Kassel) Completing a finite special string-rewriting system on the congruence class of the empty word.  ...  Summary: “Based on a polynomial-time test for determining whether a finite special string-rewriting system R is e-confluent, a procedure for completing a finite special system R on [e]z is derived.  ... 
« Previous Showing results 1 — 15 out of 1,316 results