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On quasi orders of words and the confluence property

Tero Harju, Lucian Ilie
1998 Theoretical Computer Science  
We investigate the confluence property, that is, the property of a language to contain, for any two words of it, one which is bigger, with respect to a given quasi order on the respective free monoid,  ...  This property is investigated mainly for regular and context-free ianguages.  ...  The proof of this result relies heavily on two facts: the decidability of the confluence problem w.r.t. the subword partial order of regular languages and a general confluence property of languages, as  ... 
doi:10.1016/s0304-3975(97)00259-4 fatcat:y5y6qvxnavee5hhf6ekgtxlnqy

Page 3457 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
{For the entire collection see MR 99d:68009. } 99e:68091 68Q45 68Q42 Harju, Tero (FIN-TURK; Turku); Ilie, Lucian (FIN-TURK-TC; Turku) On quasi orders of words and the confluence property.  ...  Important examples of quasi-orders on L* are the prefix, factor and subword orders.  ... 

On well quasi orders of free monoids

Lucian Ilie, Arto Salomaa
1998 Theoretical Computer Science  
We establish a number of results about the regularity and effective regularity of the down-sets, in particular, a general condition for the effective regularity of the down-set associated to an inverse  ...  Of particular languagetheoretic interest is the quasi order u <"t' (resp. u <,qu) of u being a subword (resp. a Par&h subword) of u, as well as their inverses.  ...  Acknowledgements We thank the referee for useful comments, especially as regards notations and Lemmas 4.1 and 4.4.  ... 
doi:10.1016/s0304-3975(98)00036-x fatcat:63lqzb6fdrenpnvxm37b2ic4wa

Page 6060 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
From the introduction: “In this paper, we introduce a relation Rr on w-words which is based on the notion of shuffle on w-words over w-trajectories.  ...  In this paper we introduce a stronger version of equational semantical labelling, parameterized by three choices: (1) the or- der on the underlying algebra (partial order vs. quasi-order), (2) the relation  ... 

Confluence of algebraic rewriting systems [article]

Cyrille Chenavier, Benjamin Dupont, Philippe Malbos
2021 arXiv   pre-print
These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings.  ...  The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms.  ...  Since the order ≺ P db is well-founded, it terminates in finitely many steps until we reach quasi-normal forms f and g of f and g respectively. This yields the σ-confluence of the σ-branching (a, e).  ... 
arXiv:2004.14361v4 fatcat:q53rh2ws5vh6fl3u3zqdsnjrtm

Author index volume 200 (1998)

1998 Theoretical Computer Science  
Ilie, On quasi orders of words and the confluence property Hennessy, M. and J. Rathke, Bisimulations for a calculus of broadcasting systems Illie, L., see T.  ...  ., On the algebraic structure of combinatorial problems Mattos, L.A.F., see C. Blundo Mundici, D. and N. Olivetti, Resolution and model building in the infinite-L.M., C.L. Nehaniv and R.H.  ... 
doi:10.1016/s0304-3975(98)00113-3 fatcat:pmlmy6qbezg7xhxx2z2nza35vy

Rewriting modulo isotopies in pivotal linear (2,2)-categories [article]

Benjamin Dupont
2019 arXiv   pre-print
In particular, we study the case of pivotal 2-categories using the isotopy relations given by biadjunctions on 1-cells and cyclicity conditions on 2-cells as axioms for which we rewrite modulo.  ...  We introduce a symbolic computation method in order to compute linear bases for the vector spaces of 2-cells of these categories.  ...  Quasi-orderings. Following [9] , a quasi-ordered set is a set A equipped with a transitive and reflexive binary relation on elements of A.  ... 
arXiv:1906.03904v1 fatcat:jlktlzqk6rbphkbpthilvj4mha

Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category [article]

Clément Alleaume
2016 arXiv   pre-print
We finally give an application of this theory in linear (3, 2)-polygraphs to prove a basis theorem on the category AOB with a new method using a rewriting property defined by van Ostroom: decreasingness  ...  We focus then on linear (3, 2)-polygraphs to give presentations of linear monoidal categories.  ...  ACKNOWLEDGMENTS The author would like to thank Labex Milyon (ANR-10-LABX-0070). This work has been supported by the project Cathre, ANR-13BS02-0005-02.  ... 
arXiv:1603.02592v1 fatcat:mrijmcd7hnd4lkrif4orujz57y

Bi-rewriting, a term rewriting technique for monotonic order relations [chapter]

Jordi Levy, Jaume Agustí
1993 Lecture Notes in Computer Science  
Instead of using only a rewriting relation ⊆ −→ and rewriting a to b, we use another rewriting relation ⊇  ...  We propose an extension of rewriting techniques to derive inclusion relations a ⊆ b between terms built from monotonic operators.  ...  In the following subsection we will consider the term structure in order to reduce the local confluence properties to the confluence of (extended) critical pairs.  ... 
doi:10.1007/3-540-56868-9_3 fatcat:vousksgjb5g23gcc5cwvp3vxba

Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category

Clément Alleaume
2018 Journal of Pure and Applied Algebra  
A rewriting system is said to be convergent if it is terminating and confluent.In the case of word rewriting, the property of convergence, the conjunction of termination and confluence, gives a way to  ...  We give on this partition the order ≺ such that P n ≺ P m if and only if n < m. This well-founded order respects all the properties of 4.3.1 for the critical branchings of AOB.  ...  We continue our enumeration by searching for all the overlaps of the source of i 0 2 and so on.  ... 
doi:10.1016/j.jpaa.2017.05.002 fatcat:v3yykj6dvrdhjgkcske27lzdy4

About the Design of Distributed Control Systems: The Quasi-Synchronous Approach [chapter]

Paul Caspi, Christine Mazuet, Natacha Reynaud Paligot
2001 Lecture Notes in Computer Science  
This paper focuses on the main result of the Crisys project: the quasi-synchronous approach which is based on the synchronous language Lustre-Scade.  ...  The European project Crisys " aims at improving and formalizing the actual methods, techniques and tools used in the industries concerned with process control, in order to support a global system approach  ...  Acknowledgement The authors would like to thank all the partners involved in the Crisys project.  ... 
doi:10.1007/3-540-45416-0_21 fatcat:nnito6bhofauxdh2y4k5w5mpui

Coherence of string rewriting systems by decreasingness [article]

Clément Alleaume, Philippe Malbos
2017 arXiv   pre-print
When the rewriting system is confluent and terminating, the homotopy of this complex can be characterized in term of confluence diagrams induced by the critical branchings of the rewriting system.  ...  Squier introduced a homotopical method in order to describe all the relations amongst rewriting reductions of a confluent and terminating string rewriting system.  ...  As a consequence, the multiset inclusion is a well-founded order on supports, allowing us to prove some properties by induction on the support of 2-cells. 2.1.5. Branchings.  ... 
arXiv:1612.09193v2 fatcat:vsvruff76nb6pfiavov5zb36j4

The Certification Problem Format

Christian Sternagel, René Thiemann
2014 Electronic Proceedings in Theoretical Computer Science  
Whereas CPF was originally invented to combine three different formats for termination proofs into a single one, in the meanwhile proofs for several other properties of term rewrite systems are also expressible  ...  Its acceptance is also demonstrated in international competitions: the certified tracks of both the termination and the confluence competition utilized CPF as exchange format between automated tools and  ...  In contrast, the set of techniques that are used in confluence, complexity, and termination tools is often dynamic-much of the power of these tools relies on the invention of new ways to prove these properties  ... 
doi:10.4204/eptcs.167.8 fatcat:a3jzqlr3ajgb3obnz65z3obivq

Confluence for graph transformations

N.Lafaye de Micheaux, C. Rambaud
1996 Theoretical Computer Science  
For graph rewriting Systems a notion of critical pair based only on the rewriting rules is defined. It is a generalization of the notion of critical pairs for term rewriting Systems.  ...  Using this definition, a local confluence theorem is obtained: "A graph rewriting System is locally confluent if and only if every critical pair of the System is convergent."  ...  Quasi-Order on graphs The quasi-order on graph we want to define must be an extension of the Order of the subword.  ... 
doi:10.1016/0304-3975(95)00007-0 fatcat:wjh4hpiojfbotgr7pzknncmmlu

Skew and ω-Skew Confluence and Abstract Böhm Semantics [chapter]

Zena M. Ariola, Stefan Blom
2005 Lecture Notes in Computer Science  
This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec.  ...  We present a new notion called ωskew confluence which constitutes a sufficient and necessary condition for uniqueness.  ...  We thank the anonymous referees and the editors for their comments which allowed us to make substantial improvements to the original paper.  ... 
doi:10.1007/11601548_19 fatcat:z77bts2m45fyvpnjfcdxgzrt7u
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