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Some results about confluence on a given congruence class [chapter]

Friedrich Otto
1987 Lecture Notes in Computer Science  
On the other hand, for certain subclasses of these systems confluence on a given congruence class is decidable.  ...  It is undecidable in general whether or not a term-rewriting system is confluent on a given congruence class.  ...  The author wants to thank Ron Book for bringing this problem to his attention, and for many fruitful discussions regarding the various results presented in this paper.  ... 
doi:10.1007/3-540-17220-3_13 fatcat:3lrnrib5zza6vndtefatyh6mii

Page 2221 of Mathematical Reviews Vol. , Issue 92d [page]

1992 Mathematical Reviews  
We study three decision problems on finite semi-Thue systems, namely the class equivalence problem, the word problem for the syntactic congruence of one class and the partial confluence 68Q Theory of computing  ...  A. (1-NC-C); Potter, Richard C. (1-NC-C) Term rewriting: some experimental results.  ... 

Infinite normal forms for non-linear term rewriting systems

Paola Inverardi, Monica Nesi
1995 Theoretical Computer Science  
In this paper we show that some of those results can be extended to a particular class of nonorthogonal term rewriting systems.  ...  Results about the existence of infinite normal forms have been given only for orthogonal term rewriting systems, namely left-linear and nonoverlapping systems.  ...  In [6, 14, 15] results about the existence of infinite normal forms have been given only for orthogonal term rewriting systems, namely left-linear and nonoverlapping systems.  ... 
doi:10.1016/0304-3975(94)00244-6 fatcat:opuzax752rbm3b5xkiewgcsgnu

Page 3785 of Mathematical Reviews Vol. , Issue 88g [page]

1988 Mathematical Reviews  
{For the entire collection see MR 88f:68008.} 88g:68072 68Q50 03D35 Otto, Friedrich (D-KSRL-I) Some results about confluence on a given congruence class.  ...  On the other hand, for certain subclasses of these systems confluence on a given congruence class is decidable.” {For the entire collection see MR 88f:68008.}  ... 

Confluence Modulo Equivalence with Invariants in Constraint Handling Rules [article]

Daniel Gall, Thom Frühwirth
2018 arXiv   pre-print
Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result.  ...  There is a trade-off between practical applicability and the simplicity of proving a confluence property.  ...  Introduction In program analysis, the confluence property of a program plays an important role. It ensures that any computation for a given start state results in the same final state.  ... 
arXiv:1802.03381v1 fatcat:cvds34msgbd2vkhllh5rvs6w4y

Confluence Modulo Equivalence with Invariants in Constraint Handling Rules [chapter]

Daniel Gall, Thom Frühwirth
2018 Lecture Notes in Computer Science  
Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result.  ...  There is a trade-off between practical applicability and the simplicity of proving a confluence property.  ...  Introduction In program analysis, the confluence property of a program plays an important role. It ensures that any computation for a given start state results in the same final state.  ... 
doi:10.1007/978-3-319-90686-7_8 fatcat:jj5pqncngbe6zgucfak2rchziq

Coherence for plactic monoids via rewriting theory and crystal structures [article]

Uran Meha
2021 arXiv   pre-print
This consists in starting with a convergent presentation, and expliciting a family of generating confluences to obtain a coherent presentation – one with generators, generating relations, and generating  ...  We thus obtain reduced versions of Newman's Lemma and Critical Pair Lemma, which are results for verifying convergence of a presentation.  ...  Let be a crystal monoid, say = (Γ * /∼) for some crystal Γ and a crystal congruenceon Γ * . Let 1 , 2 ∈ Γ * be representatives of 1 and 2 respectively.  ... 
arXiv:2111.11579v1 fatcat:y3impwv4zjexdbnqf55je3snwm

On deciding the confluence of a finite string-rewriting system on a given congruence class

Friedrich Otto
1987 Journal of computer and system sciences (Print)  
In general it is undecidable whether or not a given finite string-rewriting system R is confluent on a given congruence class [w]~, even when only length-reducing systems are considered.  ...  A string-rewriting system R on alphabet C induces a congruence ++ 2 on the free monoid 27 generated by Z, and hence, the set M, of congruence classes modulo -2 is a monoid.  ...  Madlener for many fruitful discussions regarding the results presented in this paper.  ... 
doi:10.1016/0022-0000(87)90017-1 fatcat:uuahdoiqerd7lmkymitfrgngd4

Page 4104 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
In this paper, the authors give a procedure that enumerates a complete set of equational unifiers for a given pair of terms under a given congruence. {For the entire collection see MR 94b:68026.}  ...  On certain classes of terms, called here ‘stable’, we prove that the resulting calculus is confluent if R is confluent, and is terminating if R is terminating.  ... 

Page 2401 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
Here results on the specification of a formal language as a finite union of congruence classes of a finite string-rewriting system, a so-called congruential language, are presented.  ...  The notation that is used throughout the mono- graph is presented, and the fundamental notions of termination, local confluence, and confluence are given. Further, some funda- mental results of M. H.  ... 

On weakly confluent monadic string-rewriting systems

K. Madlener, P. Narendran, F. Otto, L. Zhang
1993 Theoretical Computer Science  
Here a monadic string-rewriting system R on some alphabet z is called weakly confluent if it is confluent on all the congruence classes [a]s, with ao,Su {e}.  ...  It is investigated as to how far the various decidability results for finite, monadic, and confluent string-rewriting systems can be carried over to the class of finite monadic string-rewriting systems  ...  Actually, the concept of confluence on some congruence class is not completely new.  ... 
doi:10.1016/0304-3975(93)90213-d fatcat:ba7rvt2rb5fepptcymu4ql6ln4

Iterating transducers

Dennis Dams, Yassine Lakhnech, Martin Steffen
2002 The Journal of Logic and Algebraic Programming  
In this paper we give a partial algorithm to compute a finite-state transducer T * for a general class of transducers.  ...  We show how this extrapolation may be rephrased as a problem of detecting confluence properties of rewrite systems that represent the bisimulations.  ...  Given a transducer T, the relations ∼ p and ∼ f are congruences on Q * , the free monoid over the set Q of states of T.  ... 
doi:10.1016/s1567-8326(02)00025-5 fatcat:oesc7b2evvdqnmxhcjepz2n63m

Conditional rewrite rules

Stéphane Kaplan
1984 Theoretical Computer Science  
A general evaluation procedure ic; given. lntractability results about one-step rewriting, even for carlonical systems. and computation of the normal lorm function are established.  ...  For a given -+, we define the relation 1 as follows: Algebraic conditional theories The purpose of this section is to state some results on the algebraic aspect of conditional specifications.  ...  In the case of classical ruleb,, it is known that this gives rise to a large class of results, including confluency, validity of several evaluation strategies under termination hypotheses, etc.  ... 
doi:10.1016/0304-3975(84)90087-2 fatcat:r3jerbimizetdkun6ykc7joj5y

On ground-confluence of term rewriting systems

Deepak Kapur, Paliath Narendran, Friedrich Otto
1990 Information and Computation  
This undecidability result holds even when systems involving only unary function symbols and one constant are being considered, or when leftlinear or right-linear monadic systems are being considered.  ...  On the other hand, if all right-hand sides of rules of a finite Noetherian rewriting system R are either ground terms or proper subterms of the corresponding left-hand sides. then it is decidable whether  ...  Similarly, a function has the sufficient completeness property on a given set of constructors in a given equational theory, if every congruence class of ground-terms containing that function also includes  ... 
doi:10.1016/0890-5401(90)90023-b fatcat:nqqwr2x6gjdt3nxclxfm4rpffq

A fix-point characterization of Herbrand equivalence of expressions in data flow frameworks [article]

Jasine Babu, K. Murali Krishnan, Vineeth Paleri
2017 arXiv   pre-print
to the given flow graph.  ...  Most of the well-known algorithms for the computation of Herbrand equivalence in data flow frameworks proceed via iterative fix-point computation on some abstract lattice of short expressions relevant  ...  Moreover, each equivalence class in f y= * (P) is a subset of some equivalence class in the congruence P.  ... 
arXiv:1708.04976v2 fatcat:sihvysavmve3hkfrcheqesmtie
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