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Derivation Trees of Ground Term Rewriting Systems

Joost Engelfriet
1999 Information and Computation  
A notion 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.  ... 
doi:10.1006/inco.1998.2786 fatcat:ixv2ehp4pjdchk3cydhhfj34fe

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  ... 

On Term Rewriting Systems Having a Rational Derivation [chapter]

Antoine Meyer
2004 Lecture Notes in Computer Science  
Several types 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.  ... 
doi:10.1007/978-3-540-24727-2_27 fatcat:uawue3ztvrctbgjagtvk4jy7uu

Induction for positive almost sure termination

Isabelle Gnaedig
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 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.  ... 
doi:10.1145/1273920.1273943 dblp:conf/ppdp/Gnaedig07 fatcat:3rdtzrr5g5g4jpcu57475etdaq

Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

Max Dauchet, Thierry Heuillard, Pierre Lescanne, Sophie Tison
1990 Information and Computation  
The aim 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.  ... 
doi:10.1016/0890-5401(90)90015-a fatcat:qvkzgcapyzgq7ndqm4e3kmkf2e

A Proof of Weak Termination Providing the Right Way to Terminate [chapter]

Olivier Fissore, Isabelle Gnaedig, Hélène Kirchner
2005 Lecture Notes in Computer Science  
For that, we observe proof 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.  ... 
doi:10.1007/978-3-540-31862-0_26 fatcat:xhv2g5ilvbamjgx6idnfj6nit4

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.  ... 

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.  ... 

Analysis of Rewrite-Based Access Control Policies

Claude Kirchner, Hélène Kirchner, Anderson Santana de Oliveira
2009 Electronical Notes in Theoretical Computer Science  
We illustrate this general approach by the analysis 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 ).  ... 
doi:10.1016/j.entcs.2009.02.072 fatcat:q2reb4pjrrdotpxp3nwp3eq4we

Rewrite Closure for Ground and Cancellative AC Theories [chapter]

Ashish Tiwari
2001 Lecture Notes in Computer Science  
Given a binary relation IE ∪ IR on the set 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] .  ... 
doi:10.1007/3-540-45294-x_28 fatcat:e55i6hexizfpdm5gjj5czc32lu

Bottom-up tree pushdown automata: classification and connection with rewrite systems

Jean-Luc Coquidé, Max Dauchet, Rémi Gilleron, Sándor Vágvölgyi
1994 Theoretical Computer Science  
We define different types 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.  ... 
doi:10.1016/0304-3975(94)90101-5 fatcat:hesqsszixfbrhasmgojmtt26jq

System Presentation -- CARIBOO

Olivier Fissore, Isabelle Gnaedig, Hélène Kirchner
2002 Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '02  
We describe Cariboo, the implementation 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.  ... 
doi:10.1145/571157.571164 dblp:conf/ppdp/FissoreGK02 fatcat:z2vfukg7yzc6zf3snm6ubcskaq

A needed narrowing strategy

Sergio Antoy, Rachid Echahed, Michael Hanus
2000 Journal of the ACM  
It also plays an important role in the definition 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.  ... 
doi:10.1145/347476.347484 fatcat:bhoxy5lck5dyhhqyq5op45nkwq

A needed narrowing strategy

Sergio Antoy, Rachid Echahed, Michael Hanus
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 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.  ... 
doi:10.1145/174675.177899 dblp:conf/popl/AntoyEH94 fatcat:ds6ve3egtrewriav3ci4sd2v6q

Computing constructor forms with non terminating rewrite programs

Isabelle Gnaedig, Hélène Kirchner
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 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.  ... 
doi:10.1145/1140335.1140351 dblp:conf/ppdp/GnaedigK06 fatcat:pdgpkwdwubcxplpiqyjmih2jwa
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