String-Rewriting Systems

Book, Ronald V.; Otto, Friedrich

doi:10.1007/978-1-4613-9771-7

Cited by 263 publications

(76 citation statements)

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“…In this section we introduce the notions that we shall use along the paper. For more details concerning these constructions see for instance [Lot02] and [HNT05] for words and standardization, and [How95, Subsection 1.6] and [BO93] for presentations and rewriting systems.…”

Section: Preliminaries and Notationmentioning

confidence: 99%

The monoids of the patience sorting algorithm

Cain

Malheiro

Silva

2019

Int. J. Algebra Comput.

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The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences on words. Such congruences are constructed using insertion algorithms based on the concept of decreasing subsequences. Presentations for these monoids are given.Each finite-rank rPS monoid is shown to have polynomial growth and to satisfy a non-trivial identity (dependent on its rank), while the infinite rank rPS monoid does not satisfy a non-trivial identity. The lPS monoids of finite rank have exponential growth and thus do not satisfy non-trivial identities. The complexity of the insertion algorithms is discussed.rPS monoids of finite rank are shown to be automatic and to have recursive complete presentations. When the rank is 1 or 2, they are also biautomatic. lPS monoids of finite rank are shown to have finite complete presentations and to be biautomatic.

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Section: Preliminaries and Notationmentioning

confidence: 99%

The monoids of the patience sorting algorithm

Cain

Malheiro

Silva

2019

Int. J. Algebra Comput.

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“…In this section we give some basic definitions and results about rewriting systems. For more background on rewriting systems we refer the reader to [9,10].…”

Section: Preliminariesmentioning

confidence: 99%

The finite complete rewriting systems for matrix semigroup presentations

Ozer¹,

Yuksek²

2016

ija

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“…Let X be a nonterminal with val(X) = acbc ad cbc acbc acbc acbc acb|c acbc acbc acbc acb dc where '|' denotes the cut of X and val(P) = acbc acbc acbc acbc acbc. Then the occurrences of val(P) at the cut of X are (1, 1, 2, 1), (2,2,4,1), (3,3,6,1), and (4,4,8,1) where the positions in a tuple correspond to the letters in our alphabet in the order a, b, c, d. We will see later how to construct them.…”

Section: Question: Is [Val(p)] I a Factor Of [Val(t)] I ?mentioning

confidence: 99%

Compressed Decision Problems for Graph Products and Applications to (Outer) Automorphism Groups

Haubold

Lohrey

Mathissen

2012

Int. J. Algebra Comput.

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It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a restricted variant of the simultaneous compressed conjugacy problem is polynomial time Turing-reducible to the same problem for the vertex groups. A direct corollary of this result is that the word problem for the outer automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Finally, it is shown that the compressed variant of the ordinary conjugacy problem can be solved in polynomial time for right-angled Artin groups.

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String-Rewriting Systems

Cited by 263 publications

References 0 publications

The monoids of the patience sorting algorithm

The monoids of the patience sorting algorithm

The finite complete rewriting systems for matrix semigroup presentations

Compressed Decision Problems for Graph Products and Applications to (Outer) Automorphism Groups

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