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Decidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems
2008
Electronical Notes in Theoretical Computer Science
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Yi and Sakai [9] showed that the termination problem is a decidable property for the class of semi-constructor term rewriting systems, which is a superclass of the class of right ground term rewriting ...
In this paper we modify the proof of [9] to show that both innermost termination and µ-termination are decidable properties for the class of semi-constructor TRSs. ...
Acknowledgement We would like to thank the anonymous referees for their helpful comments and remarks. This work is partly supported by MEXT.KAKENHI #18500011 and #16300005. ...
doi:10.1016/j.entcs.2008.03.051
fatcat:vq6zsxszwndt3lnljdsbd5jhpa
Lazy productivity via termination
2011
Theoretical Computer Science
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We present a procedure for transforming strongly sequential constructor-based term rewriting systems (TRSs) into context-sensitive TRSs in such a way that productivity of the input system is equivalent ...
Finally, we present a simple, but fruitful extension of matrix interpretations to make them applicable for proving termination of context-sensitive TRSs. ...
Acknowledgements We thank Aart Middeldorp, Hans Zantema and the anonymous referees for valuable suggestions for improving draft versions of this paper and fruitful discussions on its topic. ...
doi:10.1016/j.tcs.2011.03.024
fatcat:akkabcwbt5cxdefk5voryqi5ca
Equational Logic and Rewriting
[chapter]
2014
Handbook of the History of Logic
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Handbook-History-Logic-Computation-EquationalLogic Handbook-History-Logic-Computation-Rewriting ...
The latter property is decidable for a confluent and terminating rewrite system. ...
In context-sensitive rewriting [108, 109] , rewriting is allowed only at some specified positions in the terms. ...
doi:10.1016/b978-0-444-51624-4.50006-x
fatcat:eqtvr66m65eula7otl7fr6ppaa
Page 5863 of Mathematical Reviews Vol. , Issue 98I
[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.
Zantema, Termination of context-sensitive rewriting (172-186); Michio Oyamaguchi and Yoshikatsu Ohta, A new parallel closed condition for Church- Rosser of left-linear term rewriting systems (187-201); ...
Sivakumar, A total, ground path ordering for proving termination of AC-rewrite sys- tems (142-156); Thomas Arts and Jiirgen Giesl, Proving innermost normalisation automatically (157-171); H. ...
Complexity Hierarchies and Higher-order Cons-free Term Rewriting
[article]
2017
arXiv
pre-print
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Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot ...
much larger classes for each type order (E^KTIME versus EXP^K-1TIME), and (iii) results for cons-free term rewriting systems have previously only been obtained for K = 1, and with additional syntactic ...
Left-linear constructor rewriting systems are very common in the literature on term rewriting. ...
arXiv:1611.10334v2
fatcat:6icowhvkqffcbjxdwvlqsax3eq
Outermost Ground Termination
2004
Electronical Notes in Theoretical Computer Science
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Our method applies in particular to systems that are non-terminating for the standard strategy nor even for the lazy strategy. a term rewriting system and the evaluation of a query consists of rewriting ...
We propose a semi-automatic inductive process to prove termination of outermost rewriting on ground term algebras. ...
Most of existing methods for proving termination of term rewriting systems (TRS in short) essentially tackle the universal termination problem: they work on free term algebras and prove termination for ...
doi:10.1016/s1571-0661(05)82535-6
fatcat:s576puihdfbmpof5xgjtk2mi3u
Strong and Weak Operational Termination of Order-Sorted Rewrite Theories
[chapter]
2014
Lecture Notes in Computer Science
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Second, we point out that the notions of irreducible term and of normal form, which coincide for unsorted rewriting are totally different for conditional rewriting and formally characterize that difference ...
rewriting systems (CTRSs) as a special case. ...
There is a 2-OSRTs R and a sort s such that the set Irr(R) s ⊆ T (F, X ) s of R-irreducible terms is not recursively enumerable, so it is not even semi-decidable if a term is R-irreducible. ...
doi:10.1007/978-3-319-12904-4_10
fatcat:h5iz6sdy25exbgbfj623bxnb4i
Developing developments
1997
Theoretical Computer Science
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Confluence results are obtained for lambda calculus with beta, eta and omega rules, lambda calculi with restricted expansion rules and for (first-and higher-order) term rewriting systems for which all ...
The class of orthogonal rewriting systems is the main class of not-necessarily-terminating, but confluent rewriting systems. ...
anymore after an W-step due to its context-sensitivity (see Example 18). ...
doi:10.1016/s0304-3975(96)00173-9
fatcat:dmhrwtsgyvel5gogpybpihkccq
Complexity of Conditional Term Rewriting
[article]
2017
arXiv
pre-print
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We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. ...
A transformation to unconditional context-sensitive rewrite systems is presented which reflects this complexity notion, as well as a technique to derive runtime and derivational complexity bounds for the ...
Acknowledgement We thank the reviewers for their detailed comments, which led to many improvements. ...
arXiv:1510.07276v5
fatcat:zrktrjs4drhuhi3uwcnlyruzna
Metalevel algorithms for variant satisfiability
2018
Journal of Logical and Algebraic Methods in Programming
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Variant satisfiability is a theory-generic algorithm to decide quantifier-free satisfiability in an initial algebra T Σ{E when the theory pΣ, Eq has the finite variant property and its constructors satisfy ...
a poset of sorts pS, ¤q; (iii) sensible OS signature; (iv) order-sorted Σalgebras and homomorphisms, and its associated category OSAlg Σ ; and (v) the construction of the term algebra T Σ and its initiality ...
Our strategy is as follows: (i) give sufficient conditions so that termination of R G corresponds to sort finiteness in Σ, (ii) define a rewrite system R F and give sufficient conditions to prove termination ...
doi:10.1016/j.jlamp.2017.12.006
fatcat:kvxues2kxjgs5bedi4gxucrbxe
Normal forms and normal theories in conditional rewriting
2016
Journal of Logical and Algebraic Methods in Programming
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, and contains the more restricted framework of conditional term rewriting systems (CTRSs) as a special case. ...
We point out that the notions of irreducible term and of normal form, which coincide for unconditional rewriting, have been conflated for conditional rewriting but are in fact totally different notions ...
We thank the anonymous referees for their constructive criticism and helpful comments. This work has been partially supported by NSF grant CNS 13-19109. ...
doi:10.1016/j.jlamp.2015.06.001
fatcat:3w34c4zp35a5bp4autbwlialzy
Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
2012
Logical Methods in Computer Science
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Unravelings are transformations from a conditional term rewriting system (CTRS, for short) over an original signature into an unconditional term rewriting systems (TRS, for short) over an extended signature ...
Finally, we show that soundness of Ohlebusch's unraveling is the weakest in soundness of the other unravelings and a transformation, proposed by Serbanuta and Rosu, for (normal) deterministic CTRSs, i.e ...
Acknowledgements We would like to thank the anonymous reviewers for their kind and useful comments to improve this paper, especially the remark in Footnote 1. ...
doi:10.2168/lmcs-8(3:4)2012
fatcat:pnme2i4hhzeinnj6d22aqwh3fq
Transformation of structure-shy programs with application to XPath queries and strategic functions
2011
Science of Computer Programming
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We discuss the application of these rewrite systems for XPath query optimization and for query migration in the context of schema evolution. ...
We show how subsets of these laws can be used to construct effective rewrite systems for specialization, generalization, and optimization of structure-shy programs. ...
Also, the transformation strategies that we composed from these laws should be better characterized in terms of the normal forms to which they lead, and in terms of their complexity and termination behaviour ...
doi:10.1016/j.scico.2010.01.003
fatcat:kz3666fm3rd4nmrpdh7gk3muha
Analytical Inductive Functional Programming
[chapter]
2009
Lecture Notes in Computer Science
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Acknowledgement The author would like to thank anonymous reviewers for their constructive and useful comments on the previous version of the paper. ...
Acknowledgements We thank the LOPSTR'2008 referees for helpful comments and suggestions. ...
Keywords: Termination, Term Rewriting Systems, Space complexity. ...
doi:10.1007/978-3-642-00515-2_7
fatcat:r3xkzawlibfcpluopvlz7ukp4y
Middle-out reasoning for synthesis and induction
1996
Journal of automated reasoning
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The planning results both in an instantiation of the program body and a plan for the veri cation of that program. ...
We have implemented these techniques as an extension of the proof planning system CL A M Bundy et al 90c], called Periwinkle, and synthesized a variety of programs fully automatically. ...
Acknowledgements We would like to thank Sophie Renault for her careful reading of this paper.
25 ...
doi:10.1007/bf00244461
fatcat:ecba53gmabh7zplgxteiy5yu5e
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