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Some results about confluence on a given congruence class
[chapter]
1987
Lecture Notes in Computer Science
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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
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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
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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
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{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
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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]
2018
Lecture Notes in Computer Science
Preserved Fulltext
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The file type is application/pdf.
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]
2021
arXiv
pre-print
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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 congruence ∼ on 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
1987
Journal of computer and system sciences (Print)
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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
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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
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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
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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
2002
The Journal of Logic and Algebraic Programming
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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
1984
Theoretical Computer Science
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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
1990
Information and Computation
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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]
2017
arXiv
pre-print
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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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