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Decidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems

Keita Uchiyama, Masahiko Sakai, Toshiki Sakabe
2008 Electronical Notes in Theoretical Computer Science  
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

Jörg Endrullis, Dimitri Hendriks
2011 Theoretical Computer Science  
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]

Claude Kirchner, Hélène Kirchner
2014 Handbook of the History of Logic  
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  
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]

Cynthia Kop, Jakob Grue Simonsen
2017 arXiv   pre-print
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

Olivier Fissore, Isabelle Gnaedig, Hélène Kirchner
2004 Electronical Notes in Theoretical Computer Science  
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]

Salvador Lucas, José Meseguer
2014 Lecture Notes in Computer Science  
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

Vincent van Oostrom
1997 Theoretical Computer Science  
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]

Cynthia Kop, Aart Middeldorp, Thomas Sternagel
2017 arXiv   pre-print
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

Stephen Skeirik, José Meseguer
2018 Journal of Logical and Algebraic Methods in Programming  
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

Salvador Lucas, José Meseguer
2016 Journal of Logical and Algebraic Methods in Programming  
, 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

Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, Aart Middeldorp
2012 Logical Methods in Computer Science  
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

Alcino Cunha, Joost Visser
2011 Science of Computer Programming  
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]

Emanuel Kitzelmann
2009 Lecture Notes in Computer Science  
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

Ina Kraan, David Basin, Alan Bundy
1996 Journal of automated reasoning  
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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