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On termination of one rule rewrite systems
1994
Theoretical Computer Science
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., On termination of one rule rewrite systems, Theoretical Computer Science 132 (1994) 3955401. ...
In particular, Dauchet proves the undecidability of the termination of one rule rewrite systems by coding Turing machines into one rule rewrite systems. ...
Reduction of the termination of one rule rewrite systems to the termination of semi-Thue systems Let us call abstract machines rewrite systems where rules are all of the form and where sl, . . . , s,, ...
doi:10.1016/0304-3975(94)00029-8
fatcat:blq7jlcworac7kkkl3kdfel3be
Termination and derivational complexity of confluent one-rule string-rewriting systems
2001
Theoretical Computer Science
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develop techniques to attack the termination and complexity problems of con uent one-rule string-rewriting systems. ...
It is not known whether the termination problem is decidable for one-rule string-rewriting systems, though the con uence of such systems is decidable by Wrathall (in: Word Equations and In this paper we ...
One-rule string-rewriting systems are thus considered to be the most simple example of rewriting systems. ...
doi:10.1016/s0304-3975(00)00367-4
fatcat:bleuisb22zajnlx6oqtbjwupni
Page 3206 of Mathematical Reviews Vol. , Issue 98E
[page]
1998
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Basically, termination of a rewrite system R is proved by means of termination of a simplified rewrite system S and an auxiliary rewrite system U connecting R and S. ...
In fact, we show that the Knuth-Bendix completion procedure always terminates when ap- plied to prefix-rewriting systems on virtually free presentations of context-free groups. ...
Termination modulo equations by abstract commutation with an application to iteration
1997
Theoretical Computer Science
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Hence, the only sensible strategy to prove termination of such a rewrite system is to transform it into a rewrite system without self-embedding rules, for which termination can be derived. ...
Again this rewrite system contains self-embedding rules. ...
Basically, termination of a rewrite system R is proved by means of termination of a simplified rewrite system S and an auxiliary rewrite system U connecting R and S. ...
doi:10.1016/s0304-3975(96)00254-x
fatcat:j3d36b7omfh4doauzyf7t24umq
Commutation, transformation, and termination
[chapter]
1986
Lecture Notes in Computer Science
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In this paper we study the use of commutation properties for proving termination of rewrite systems. ...
Commutation properties may be used to prove termination of a combined system RUS by proving termination of R and S separately. ...
A rewrite system is any set R of rewrite rules. ...
doi:10.1007/3-540-16780-3_76
fatcat:czdyqo6gubf7hniihajvrcviwm
Persistence Of Termination For Term Rewriting Systems With Ordered Sorts
2007
Zenodo
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Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. ...
In this paper, we show that the Zantema's result can be extended to term rewriting systems on ordered sorts, i.e., termination is persistent for term rewriting systems on ordered sorts without collapsing ...
The notion of termination for rewrite systems corresponds to the existence of answers of computations. So termination is the fundamental notion of term rewriting systems as computation models [7] . ...
doi:10.5281/zenodo.1081045
fatcat:e5elhfr6knewvcjvlmo7htjere
Simulation as a correct transformation of rewrite systems
[chapter]
1997
Lecture Notes in Computer Science
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Kamperman and Walters proposed the notion of a simulation of one rewrite system by another one, whereby each term of the simulating rewrite system is related to a term in the original rewrite system. ...
In this paper it is shown that if such a simulation is sound and complete and preserves termination, then the transformation of the original into the simulating rewrite system constitutes a correct step ...
Recently, Kamperman and Walters [7, 8, 6) proposed a notion of simulation of one rewrite system by another rewrite system. ...
doi:10.1007/bfb0029968
fatcat:d5fasnjdh5g6tauk62oqnnegfu
Simulation of SOS definitions with term rewriting systems
[chapter]
1994
Lecture Notes in Computer Science
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Since only standard unconditional rewrite rules are used, every theorem prover based on rewriting can be employed to implement this kind of semantics definitions, and so to reason about them. ...
This paper presents a method to transform a structured operational semantics (SOS) definition 8, given by a special form of deduction system, into a term rewriting system 7~. ...
of rewrite systems. ...
doi:10.1007/3-540-57880-3_10
fatcat:cy2hxwvttvazrigvp2nazfdyaq
Transforming Cycle Rewriting into String Rewriting
2015
International Conference on Rewriting Techniques and Applications
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Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. ...
We present new techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. ...
We thank Johannes Waldmann for fruitful remarks, in particular for his suggestions leading to Section 4 on trace decreasing matrix interpretations. ...
doi:10.4230/lipics.rta.2015.285
dblp:conf/rta/SabelZ15
fatcat:huejxncs6bbhtmjhckkcglqyo4
An on-line problem database
[chapter]
1998
Lecture Notes in Computer Science
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For the current proceedings, the main subjects were Term rewriting systems Symbolic and algebraic computation Uni cation and matching Completion techniques String and graph rewriting Conditional and typed ...
The RTA list seeks to summarize open problems and subsequent solutions in elds of interest to this conference. ...
Termination is undecidable for nonlength-increasing monadic systems of rules 7 . For one monadic rule, con uence is decidable 37,83 . What about con uence of one nonmonadic rule? ...
doi:10.1007/bfb0052380
fatcat:x57lyotlxrh5bdan42az6tileq
Problems in rewriting III
[chapter]
1995
Lecture Notes in Computer Science
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The union of two totally terminating rewrite systems which do not share any symbols is totally terminating if at least one of them does not contain a rule that has more occurrences of some variable on ...
Termination of string-rewriting systems is known to be undecidable [49] . Termination of a single term-rewriting rule was proved undecidable in [32; 64] . ...
doi:10.1007/3-540-59200-8_82
fatcat:in5aspimbrbvngnrhzcm7tfwei
Confluent term rewriting systems with membership conditions
[chapter]
1988
Lecture Notes in Computer Science
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We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution ...
We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear. ...
A term rewriting system R on T is a reduction system R = (T, --~) such that the reduction relation --* is defined by a set t> of rewriting rules on T. If R has Mt ~, Mr, then we write Ms ~> M~ E R. ...
doi:10.1007/3-540-19242-5_17
fatcat:rkyoyv3ibvfq5aticm735dvtgq
Hierarchical termination
[chapter]
1995
Lecture Notes in Computer Science
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Some (largely syntactic) sufficient conditions are given here for the union of terminating rewrite systems to be terminating, particularly in the hierarchical case, when one of the systems makes no reference ...
-A left-linear system has no rule with more than one occurrence of a variable on its left-hand side. ...
to first apply the green rule as many times as necessary to rewrite the (one or more) occurrences of that variable on the left-hand side of the purple rule, followed by the same purple step. ...
doi:10.1007/3-540-60381-6_6
fatcat:2cpjqo6k6nhetdb7nhuf2kxm2u
When are two rewrite systems more than none?
[chapter]
1997
Lecture Notes in Computer Science
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We present some old and new su cient conditions under which termination existence of normal forms, regardless of computation strategy and con uence uniqueness are preserved by s u c h c o m binations. ...
We look at non-deterministic programs expressed as termrewriting systems which compute normal forms of input terms and consider the case where individual systems share constructors, but not de ned symbols ...
the top of the left side of a rule of one system are prohibited from also appearing at the top left of a rule in the conjoined system. ...
doi:10.1007/bfb0029947
fatcat:g7qrw35qljgy5dzqo7zxh4t45u
From Conditional to Unconditional Rewriting
[chapter]
2005
Lecture Notes in Computer Science
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An automated technique to translate conditional rewrite rules into unconditional ones is presented, which is suitable to implement, or compile, conditional rewriting on top of much simpler and easier to ...
optimize unconditional rewrite systems. ...
The algorithm above, taking a conditional Σ-rewrite system R and a Σ-term α as input, terminates iff R terminates on α. ...
doi:10.1007/978-3-540-31959-7_13
fatcat:iirh3zqu4jfcteosiw4rwk64oe
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