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Geodesic Rewriting Systems and Pregroups
[chapter]
2010
Combinatorial and Geometric Group Theory
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We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups. ...
We show that these are well-behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. ...
The Knuth-Bendix procedure really depends on the chosen ordering . ...
doi:10.1007/978-3-7643-9911-5_3
fatcat:2kt4ma2ztbfbzmkiiqiwff5tta
The development of the theory of automatic groups
[article]
2022
arXiv
pre-print
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properties for groups in some infinite families (braid groups, mapping class groups, families of Artin groups, and Coxeter groups). ...
We explain how actions of groups on spaces displaying various notions of negative curvature can be used to prove automaticity or biautomaticity, and show how these results have been used to derive these ...
The next step is to run the Knuth-Bendix procedure for a while on R. ...
arXiv:2205.14911v1
fatcat:4uoexxymnfcj5i4f5lcsz7m4cm
Reference list of indexed articles
1995
Theoretical Computer Science
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Watson, Solving divergence in Knuth-Bendix
completion by enriching signatures
112 (1) (1993) 145-185
161. T. Herbst and R.M. ...
Smale, Separation of complexity classes in Koiran's weak model 133 (I) (1994) 3-14 522. T. Emerson, Relativizations of the P =? ...
doi:10.1016/0304-3975(95)90002-0
fatcat:b7nmywx4tff6lhcd3jkoagotrm
Category Theory Framework for Variability Models with Non-Functional Requirements
2021
Zenodo
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The ones that apply to our work, in order of usage, are: automated theorem prover with Knuth-Bendix completion [26] for logic and equations, and hashing, balanced trees and chasing for data-type and ...
Informally speaking, a category C is any collection of objects representing spaces that can be related to each other via arrows (i.e., morphisms). ...
doi:10.5281/zenodo.4599584
fatcat:jm2e5k77rbbt5ko3nisto3quua
Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
[article]
2012
arXiv
pre-print
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If we allow plugging input and output wires together, we can intuitively represent complex compositions of processes, formalised as morphisms in a monoidal category. [...] ...
Expanding · and · using the dualiser, we obtain the following expression for the Frobenius algebra
Knuth-Bendix completion for string graphs Knuth-Bendix completion is a procedure for turning terminating ...
Knuth-Bendix completion takes a rewrite system R and a strict, total reduction ordering ω on terms, and operates as follows: 1. Compute all of the critical pairs for R. 2. ...
arXiv:1203.0202v2
fatcat:zx2s4qevsre53ecyigq6bnhjhe
Polynomial Path Orders
2013
Logical Methods in Computer Science
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On the other hand POP* provides an order-theoretic characterisation of the polytime computable functions: the polytime computable functions are exactly the functions computable by an orthogonal constructor ...
We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two related, but distinct contexts. ...
For instance, the Knuth-Bendix order [14] can be miniaturised to characterise linear space [20] . ...
doi:10.2168/lmcs-9(4:9)2013
fatcat:dwikxzghx5dojfhakj7qkz24xq
Reference list of indexed articles
1995
Theoretical Computer Science
Preserved Fulltext
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Watson, Solving divergence m Knuth-Bendix
completion by enriching signatures
112 (1) (1993) 145-185
161. T. Herbst and R.M. ...
A very hard log-space counting class
107 (1) (1993) 3 -30
88. M-program
model
107 (1)
(1993) 31 61
89. R decision tree complexity
107 (1) (1993) 63 76
90. K.-J. Lange. ...
doi:10.1016/0304-3975(95)80003-4
fatcat:5nnk76aalje5potfoeg7hksbce
Automated Verification of Relational While-Programs
[chapter]
2014
Lecture Notes in Computer Science
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Prover9 implements a first-order resolution and paramodulation calculus. Equalities are handled via rewriting rules and Knuth-Bendix completion. ...
For example, the latter three characterise S as transitive, antisymmetric, and total (sometimes also called complete); hence as a linear order. ...
doi:10.1007/978-3-319-06251-8_11
fatcat:hjdc3zloovhgnctwp62pha3ysi
Computing group resolutions
2004
Journal of symbolic computation
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We describe an algorithm for constructing a reasonably small CW-structure on the classifying space of a finite or automatic group G. ...
General methods for calculating cohomology of finitely generated infinite groups tend to involve Gröbner bases or Knuth-Bendix type rewrite methods. ...
The procedure of Brown and Razak Salleh has been implemented by Heyworth and Wensley (2003) using a logged Knuth-Bendix algorithm and Gröbner basis techniques. ...
doi:10.1016/j.jsc.2004.03.003
fatcat:imki4ka2vbdeddvhxi6ys6grdu
String Diagram Rewrite Theory I: Rewriting with Frobenius Structure
[article]
2022
arXiv
pre-print
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It also provides techniques such as Knuth-Bendix completion [KB70] that turn ill-behaved rewriting systems into well-behaved ones. ...
As shown in the sequel to this paper (after [BGK + 17, BGK + 21]), DPOI enjoys the Knuth-Bendix property: joinability of critical pairs is the same as local confluence. ...
arXiv:2012.01847v2
fatcat:5defrofqqrhm7aiqtzb4pkywfi
Polynomial Path Orders: A Maximal Model
[article]
2012
arXiv
pre-print
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As an application in the context of ICC we provide an order-theoretic characterisation of the polytime computable functions. ...
We introduce a novel path order with multiset status, the polynomial path order POP*. ...
Similar, multiset path orders (MPO for short) induce primitive recursive complexity [24] , the induced bound for the Knuth-Bendix order is two-recursive [31] and for lexicographic path orders it is ...
arXiv:1209.3793v1
fatcat:lvm5673ln5drxms3z4eap5omju
4 Computational modal logic
[chapter]
2007
Studies in Logic and Practical Reasoning
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Concerning the ordering , state-of-the-art first-order theorem provers standardly contain implementations of recursive path orderings, lexicographic path orderings or Knuth Bendix orderings, which are ...
Refinements of the particular ordering defined in Section 3.1 can be obtained by either recursive path orderings or Knuth Bendix orderings (definitions of orderings and ordering extensions can be found ...
doi:10.1016/s1570-2464(07)80007-3
fatcat:zrhdgzcgovfc3lxuuqnjpsa5bi
Symmetries in Reversible Programming: From Symmetric Rig Groupoids to Reversible Programming Languages
[article]
2021
arXiv
pre-print
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The automatic Knuth and Bendix [1970] completion produced too many equations making proving correctness and termination intractable. ...
Since BAut( ) is a univalent subuniverse, we can characterise its path space. ...
arXiv:2110.05404v1
fatcat:5lwu7nxrwna5thzngtuvv43og4
Automatic semigroups vs automaton semigroups
[article]
2018
arXiv
pre-print
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It provides what appears to be the first known connection from a class of automatic semigroupsto a class of automaton semigroups. ...
semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a language of greedy normal forms under one-sided multiplication.The framework embraces many of the well-known classes ...
Whatever the way a quadratic normalisation is obtained (brute force, Garside theory, Knuth-Bendix completion, etc), to compute its breadth and to check Condition ( ) remain low-cost. ...
arXiv:1609.09364v5
fatcat:ux7yplt7ovd6vacjixvnjgw444
Algorithms in Philosophy, Informatics and Logic. A Position Manifesto 2017
2017
IfColog journal of logics and their applications (FLAP)
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See [Knuth & Bendix, 1970] for the Knuth-Bendix completion procedure.199 See[Ganzinger & Stuber, 1992] for such a system. ...
§ 6.2.1. 141 This has the advantage that we could take any well-founded ordering that is total on ground terms and run the terminating ground version of a Knuth-Bendix completion procedure [Knuth ...
In [Hutter, 1994] , there is synthesis of induction orderings by rippling (cf. § 7.2). ...
dblp:journals/flap/GabbayS17
fatcat:wvtsqquk3vhm3ohgsxn6lzc22u
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