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

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. ...

##
###
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

1995
*
Theoretical Computer Science
*

In this paper we show that

doi:10.1016/0304-3975(94)00244-6
fatcat:opuzax752rbm3b5xkiewgcsgnu
*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. ...##
###
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]

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. ...

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

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. ...

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

2021
*
arXiv
*
pre-print

This consists in starting with

arXiv:2111.11579v1
fatcat:y3impwv4zjexdbnqf55je3snwm
*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*congruence*∼*on*Γ * . Let 1 , 2 ∈ Γ * be representatives of 1 and 2 respectively. ...##
###
On deciding the confluence of a finite string-rewriting system on a given congruence class

1987
*
Journal of computer and system sciences (Print)
*

In general it is undecidable whether or not

doi:10.1016/0022-0000(87)90017-1
fatcat:uuahdoiqerd7lmkymitfrgngd4
*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. ...##
###
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

1993
*
Theoretical Computer Science
*

Here

doi:10.1016/0304-3975(93)90213-d
fatcat:ba7rvt2rb5fepptcymu4ql6ln4
*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. ...##
###
Iterating transducers

2002
*
The Journal of Logic and Algebraic Programming
*

In this paper we give

doi:10.1016/s1567-8326(02)00025-5
fatcat:oesc7b2evvdqnmxhcjepz2n63m
*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. ...##
###
Conditional rewrite rules

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. ...

##
###
On ground-confluence of term rewriting systems

1990
*
Information and Computation
*

This undecidability

doi:10.1016/0890-5401(90)90023-b
fatcat:nqqwr2x6gjdt3nxclxfm4rpffq
*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 ...##
###
A fix-point characterization of Herbrand equivalence of expressions in data flow frameworks
[article]

2017
*
arXiv
*
pre-print

to the

arXiv:1708.04976v2
fatcat:sihvysavmve3hkfrcheqesmtie
*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. ...
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