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Geodesic Rewriting Systems and Pregroups [chapter]

Volker Diekert, Andrew J. Duncan, Alexei G. Myasnikov
2010 Combinatorial and Geometric Group Theory  
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]

Sarah Rees
2022 arXiv   pre-print
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  
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

Daniel-Jesus Munoz, Dilian Gurov, Monica Pinto, Lidia Fuentes
2021 Zenodo  
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]

Aleks Kissinger
2012 arXiv   pre-print
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

Martin Avanzini, Georg Moser, Franz Baader
2013 Logical Methods in Computer Science  
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  
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]

Rudolf Berghammer, Peter Höfner, Insa Stucke
2014 Lecture Notes in Computer Science  
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

Graham Ellis
2004 Journal of symbolic computation  
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]

Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi
2022 arXiv   pre-print
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]

Martin Avanzini, Georg Moser
2012 arXiv   pre-print
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]

Ian Horrocks, Ullrich Hustadt, Ulrike Sattler, Renate Schmidt
2007 Studies in Logic and Practical Reasoning  
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]

Vikraman Choudhury, Jacek Karwowski, Amr Sabry
2021 arXiv   pre-print
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]

Matthieu Picantin
2018 arXiv   pre-print
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

Dov M. Gabbay, Jörg H. Siekmann
2017 IfColog journal of logics and their applications (FLAP)  
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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