The word problem for Thue rewriting systems

1995 ◽  
pp. 27-38 ◽  
Author(s):  
Gerard Lallement
Keyword(s):  
Word Problem ◽  
Rewriting Systems

REWRITING SYSTEMS IN ALTERNATING KNOT GROUPS

2006 ◽  
Vol 16 (04) ◽  
pp. 749-769 ◽  
Author(s):  
FABIENNE CHOURAQUI
Keyword(s):  
Word Problem ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Regular Position

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the augmented Dehn presentation of the knot group of a tame, prime, alternating knot in regular position, with a common projection has a finite and complete rewriting system. This provides an algorithm for solving the word problem with this presentation and we find an algorithm for solving the word problem with the Dehn presentation also.

Finite complete rewriting systems and the complexity of the word problem

1984 ◽  
Vol 21 (5) ◽  
pp. 521-540 ◽  
Author(s):  
G. Bauer ◽  
F. Otto
Keyword(s):  
Word Problem ◽  
Rewriting Systems

scholarly journals Polygraphs of finite derivation type

2016 ◽  
Vol 28 (2) ◽  
pp. 155-201 ◽  
Author(s):  
YVES GUIRAUD ◽  
PHILIPPE MALBOS
Keyword(s):  
Word Problem ◽  
Finiteness Condition ◽  
Necessary Condition ◽  
Finiteness Property ◽  
Rewriting Systems ◽  
Higher Dimensional ◽  
String Rewriting ◽  
Finite Derivation Type ◽  
Finitely Presented ◽  
Finite Presentations

Craig Squier proved that, if a monoid can be presented by a finite convergent string rewriting system, then it satisfies the homological finiteness condition left-FP3. Using this result, he constructed finitely presentable monoids with a decidable word problem, but that cannot be presented by finite convergent rewriting systems. Later, he introduced the condition of finite derivation type, which is a homotopical finiteness property on the presentation complex associated to a monoid presentation. He showed that this condition is an invariant of finite presentations and he gave a constructive way to prove this finiteness property based on the computation of the critical branchings: Being of finite derivation type is a necessary condition for a finitely presented monoid to admit a finite convergent presentation. This survey presents Squier's results in the contemporary language of polygraphs and higher dimensional categories, with new proofs and relations between them.

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