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Derivation Trees of Ground Term Rewriting Systems

1999
*
Information and Computation
*

A notion

doi:10.1006/inco.1998.2786
fatcat:ixv2ehp4pjdchk3cydhhfj34fe
*of**derivation**tree*is introduced for*ground**term**rewriting**systems*and new proofs are given for some old results. ... Acknowledgement I thank Jurriaan Hage for his comments on a previous version*of*this paper. I thank the referee for several constructive remarks. ... Introduction A*ground**term**rewriting**system*is a*term**rewriting**system**of*which the rules do not contain variables. ...##
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Page 9546 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

This is because the set

*of*all reducible*ground**terms*is a regular*tree*language for every left-linear*term**rewrite**system*R. ... The joinability result leads to poly- nomial time algorithms for: local confluence*of**ground**rewrite**systems*, confluence*of*terminating*ground**rewrite**systems*, and completeness*of**ground**rewrite**systems*...##
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On Term Rewriting Systems Having a Rational Derivation
[chapter]

2004
*
Lecture Notes in Computer Science
*

Several types

doi:10.1007/978-3-540-24727-2_27
fatcat:uawue3ztvrctbgjagtvk4jy7uu
*of**term**rewriting**systems*can be distinguished by the way their rules overlap. ... Our aim is to study the*derivation*relation*of*such*systems*(i.e. the reflexive and transitive closure*of*their*rewriting*relation) and, if possible, to provide a finite mechanism characterizing it. ...*Derivation**of*Suffix*Systems*This section presents a study*of*the*derivation*relations*of*suffix*term**rewriting**systems*. ...##
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Induction for positive almost sure termination

2007
*
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '07
*

The proof is developed in generating proof

doi:10.1145/1273920.1273943
dblp:conf/ppdp/Gnaedig07
fatcat:3rdtzrr5g5g4jpcu57475etdaq
*trees*, modelizing*rewriting**trees*, in alternatively applying abstraction steps, expressing the application*of*the induction hypothesis, and narrowing steps, simulating ... This technique can be fully automatized, in particular for*rewrite**systems*on constants, very useful to modelize probabilistic protocols. ... Acknowledgments We would like to thank Olivier Bournez for fruitful discussions on termination*of*probabilistic*rewriting*and on this paper, and for giving us motivating examples. ...##
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Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

1990
*
Information and Computation
*

The aim

doi:10.1016/0890-5401(90)90015-a
fatcat:qvkzgcapyzgq7ndqm4e3kmkf2e
*of*this paper is to propose an algorithm to decide the confluence*of*finite*ground**term**rewrite**systems*. ... Actually a more general class*of*possibly infinite*ground**term**rewrite**systems*is studied. ...*GROUND**TREE*TRANSDUCERS In this section, we define a special type*of**tree*automata called*ground**tree*transducers, to simulate the behavior*of**ground**term**rewrite**systems*. ...##
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A Proof of Weak Termination Providing the Right Way to Terminate
[chapter]

2005
*
Lecture Notes in Computer Science
*

For that, we observe proof

doi:10.1007/978-3-540-31862-0_26
fatcat:xhv2g5ilvbamjgx6idnfj6nit4
*trees*built from the*rewrite**system*, schematizing the innermost*rewriting**tree**of*any*ground**term*, and generated with two mechanisms: abstraction, schematizing normalization ... Then, we show how, for any*ground**term*, a normalizing*rewriting*strategy can be extracted from the proof*trees*, even if the*ground**term*admits infinite*rewriting**derivations*. f (g(X7), g(X7)) Abstract ... The schematization*of**ground**rewriting**derivation**trees*is achieved through constraints. ...##
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Page 1063 of Mathematical Reviews Vol. , Issue 91B
[page]

1991
*
Mathematical Reviews
*

Summary: “We prove that (1) it is undecidable whether a

*term*-*rewriting**system*preserves recognizability, and (2)*ground**term*-*rewriting**systems*with recognizable control are as powerful as general*rewriting*... Due to this close relationship to (*derivation*)*trees*, the graph languages gener- ated can be described in*terms**of*regular*tree*languages and regular string languages. ...##
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Page 1592 of Mathematical Reviews Vol. , Issue 92c
[page]

1992
*
Mathematical Reviews
*

Summary: “We present a new result on the relationship between

*term**rewriting**systems*and regular*tree*languages. ... In particular, we show how an incremental termination proof for a*term**rewriting**system*7 can be used to*derive*upper bounds on the length*of**derivations*in. 7. ...##
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Analysis of Rewrite-Based Access Control Policies

2009
*
Electronical Notes in Theoretical Computer Science
*

We illustrate this general approach by the analysis

doi:10.1016/j.entcs.2009.02.072
fatcat:q2reb4pjrrdotpxp3nwp3eq4we
*of*a firewall*system*policy. ... The*rewrite*-based approach provides executable specifications for security policies, which can be independently designed, verified, and then anchored on programs using a modular discipline. ... Given a terminating*rewrite**system*R, let us consider N , the subset*of*normalized*ground*instances*of**terms*in T (F, X ). ...##
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Rewrite Closure for Ground and Cancellative AC Theories
[chapter]

2001
*
Lecture Notes in Computer Science
*

Given a binary relation IE ∪ IR on the set

doi:10.1007/3-540-45294-x_28
fatcat:e55i6hexizfpdm5gjj5czc32lu
*of**ground**terms*over some signature, we define an abstract*rewrite*closure for IE ∪ IR. ... An abstract*rewrite*closure can be interpreted as a specialized*ground**tree*transducer (pair*of*bottom-up*tree*automata) and can be used to efficiently decide the reachability relation → * I E∪I E − ∪I ... Such a pair defines a binary relation → * E∪F • ← * E∪B − on the set*of**ground**terms*and is called a "*ground**tree*transducer" in the*tree*automata literature [8] . ...##
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Bottom-up tree pushdown automata: classification and connection with rewrite systems

1994
*
Theoretical Computer Science
*

We define different types

doi:10.1016/0304-3975(94)90101-5
fatcat:hesqsszixfbrhasmgojmtt26jq
*of*bottom-up*tree*pushdown automata and study their connections with*rewrite**systems*. ... Using the decidability*of**ground*reducibility, we prove the decidability*of*the trf property. ... Theorem 4.15 associates with each convergent left-linear*term**rewriting**system*a deterministic tpda computing normal forms*of**ground**terms*. ...##
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System Presentation -- CARIBOO

2002
*
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '02
*

We describe Cariboo, the implementation

doi:10.1145/571157.571164
dblp:conf/ppdp/FissoreGK02
fatcat:z2vfukg7yzc6zf3snm6ubcskaq
*of*an inductive process recently proposed to prove termination*of**rewriting*under strategies on*ground**term*algebras. ... The method is based on an abstraction mechanism, introducing variables that represent*ground**terms*in normal form, and on narrowing, schematizing reductions on*ground**terms*. ... [4] , where a program is a*term**rewriting**system*and the evaluation*of*a query consists in*rewriting*a*ground*expression. ...##
###
A needed narrowing strategy

2000
*
Journal of the ACM
*

It also plays an important role in the definition

doi:10.1145/347476.347484
fatcat:bhoxy5lck5dyhhqyq5op45nkwq
*of*some algorithms*of*unification modulo equational theories which are defined by confluent*term**rewriting**systems*. ... Our strategy is sound and complete for a large class*of**rewrite**systems*, is optimal w.r.t. the cost measure that counts the number*of*distinct steps*of*a*derivation*, computes only incomparable and disjoint ... Acknowledgement The authors are grateful to the anonymous referees for their helpful remarks to improve the final version*of*this paper. ...##
###
A needed narrowing strategy

1994
*
Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '94
*

It also plays an important role in the definition

doi:10.1145/174675.177899
dblp:conf/popl/AntoyEH94
fatcat:ds6ve3egtrewriav3ci4sd2v6q
*of*some algorithms*of*unification modulo equational theories which are defined by confluent*term**rewriting**systems*. ... Our strategy is sound and complete for a large class*of**rewrite**systems*, is optimal w.r.t. the cost measure that counts the number*of*distinct steps*of*a*derivation*, computes only incomparable and disjoint ... Acknowledgement The authors are grateful to the anonymous referees for their helpful remarks to improve the final version*of*this paper. ...##
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Computing constructor forms with non terminating rewrite programs

2006
*
Proceedings of the 8th ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '06
*

We propose an inductive procedure proving C-reducibility

doi:10.1145/1140335.1140351
dblp:conf/ppdp/GnaedigK06
fatcat:pdgpkwdwubcxplpiqyjmih2jwa
*of**rewriting*. The*rewriting*relation on*ground**terms*is simulated through an abstraction mechanism and narrowing. ...*derivations*. ... A*ground**term*is (innermost) (strongly) C-reducible iff it reduces into a C-*term*on at least one*of*its (resp. all) (innermost)*rewriting**derivations*. ...
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