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Context Unification and Traversal Equations [chapter]

Jordi Levy, Mateu Villaret
2001 Lecture Notes in Computer Science  
This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular  ...  Context unification was originally defined by H. Comon in ICALP'92, as the problem of finding a unifier for a set of equations containing first-order variables and context variables.  ...  Bonet for her valuable comments and suggestions, and all the anonymous referees.  ... 
doi:10.1007/3-540-45127-7_14 fatcat:jgdadztljjaanhir4743jswy2e

On the relation between Context and Sequence Unification

Temur Kutsia, Jordi Levy, Mateu Villaret
2010 Journal of symbolic computation  
Both Sequence and Context Unification generalize the same problem: Word Unification.  ...  Context Unification deals with the same problem for ranked terms involving context variables, and has applications in computational linguistics and program transformation.  ...  That proof was based on the use of traversals of terms, and on traversal equations. These traversal equations were reduced to word equations with regular constraints.  ... 
doi:10.1016/j.jsc.2009.07.001 fatcat:kubunxx7czg5lmkk4a27hiycci

Source-Tracking Unification [chapter]

Venkatesh Choppella, Christopher T. Haynes
2003 Lecture Notes in Computer Science  
Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming.  ...  We propose a path-based framework for deriving and simplifying source-tracking information for firstorder term unification in the empty theory.  ...  be traversed in either direction.  ... 
doi:10.1007/978-3-540-45085-6_39 fatcat:56ievgbgqnfcxhbo5hx56bd66m

Source-tracking unification

Venkatesh Choppella, Christopher T. Haynes
2005 Information and Computation  
Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming.  ...  We propose a path-based framework for deriving and simplifying source-tracking information for firstorder term unification in the empty theory.  ...  be traversed in either direction.  ... 
doi:10.1016/j.ic.2004.10.013 fatcat:sg4x4pzierg3tgrqefcq5bchce

Page 1309 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
This is done by reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permuta- tions), and then reducing traversal equations to word equations with  ...  “In this paper, we prove that, if the so-called rank-bound conjec- ture is true, then the context unification problem is decidable.  ... 

Page 4109 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
Difference match- ing allows us to use rippling in other contexts, e.g., equational, inequational, and propositional reasoning.  ...  (D-MNCH; Munich) Unification in the union of disjoint equational theories: combining decision procedures.  ... 

Traversable wormholes supported by cosmic accelerated expanding equations of state [article]

Francisco S. N. Lobo
2006 arXiv   pre-print
Chaplygin gas, and the van der Waals quintessence equation of state.  ...  We explore the possibility that traversable wormholes be supported by specific equations of state responsible for the present accelerated expansion of the Universe, namely, phantom energy, the generalized  ...  [2] [3] [4] Secondly, the generalized Chaplygin gas (GCG) is a candidate for the unification of dark energy and dark matter, and is parametrized by an exotic equation of state given by p ch = −A/ρ α  ... 
arXiv:gr-qc/0611150v1 fatcat:p4m54q6se5aofd65wkl6mi3lva

Page 22 of Computational Linguistics Vol. 26, Issue 4 [page]

2000 Computational Linguistics  
Assuming instead that a recursive traversal of the QLF is involved, then this particular unification equation will be formed and solved entirely within the scope of the lambda binding x.  ...  john,y), but in this expression, y really is free and so we do not have a valid equation.  ... 

Practical Higher-Order Pattern Unification with On-the-Fly Raising [chapter]

Gopalan Nadathur, Natalie Linnell
2005 Lecture Notes in Computer Science  
An important characteristic of such problems is that they are given by equations appearing under a prefix of alternating universal and existential quantifiers.  ...  Higher-order pattern unification problems arise often in computations carried out within systems such as Twelf, λProlog and Isabelle.  ...  Acknowledgements This work began while the first author was on a sabbatical visit to the Protheo group at LORIA and INRIA, Nancy and the Comete and Parsifal groups at Ecole Polytechnique and INRIA, Saclay  ... 
doi:10.1007/11562931_28 fatcat:6tr7ribftjb4ppsvtfxsf4zvbq

TRAVERSABLE WORMHOLES SUPPORTED BY COSMIC ACCELERATED EXPANDING EQUATIONS OF STATE

FRANCISCO S. N. LOBO
2008 The Eleventh Marcel Grossmann Meeting  
Chaplygin gas, and the van der Waals quintessence equation of state.  ...  We explore the possibility that traversable wormholes be supported by specific equations of state responsible for the present accelerated expansion of the Universe, namely, phantom energy, the generalized  ...  [2] [3] [4] Secondly, the generalized Chaplygin gas (GCG) is a candidate for the unification of dark energy and dark matter, and is parametrized by an exotic equation of state given by p ch = −A/ρ α  ... 
doi:10.1142/9789812834300_0359 fatcat:rlokxbxrvzfujlb3xu6d5hhkqu

Unification and Matching on Compressed Terms [article]

Adrià Gascón, Guillem Godoy, Manfred Schmidt-Schauß
2010 arXiv   pre-print
The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton  ...  For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.  ...  The context matching problem is a particular case of context unification where one of the sides of each equation in ∆ is ground.  ... 
arXiv:1003.1632v1 fatcat:wjvugw56y5g3vkpz6lmq2opctq

Page 8490 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
programs (154-168); Jordi Levy and Mateu Villaret, Context uni- fication and traversal equations (169-184); Sébastien Limet, Pierre Réty and Helmut Seidl, Weakly regular relations and applications (185  ...  , Goal-directed E-unification (231-245); Michio Oyamaguchi and Yoshikatsu Ohta, The unification prob- lem for confluent right-ground term rewriting systems (246-260); Femke van Raamsdonk, On termination  ... 

Processing Textbook-Style Matrices [chapter]

Alan Sexton, Volker Sorge
2006 Lecture Notes in Computer Science  
Given an underspecified matrix containing ellipses and fill symbols, our algorithm extracts the semantic information contained.  ...  We present an algorithm that provides the interface between the textbook style representation of matrix expressions and their concrete interpretation as formal mathematical objects.  ...  Each edge in the graph will carry two weights: the horizontal cost of traversing the edge and the vertical cost of traversing it.  ... 
doi:10.1007/11618027_8 fatcat:o4luat3vyvfvpl7lvesusxm4kq

Linear Second-Order Unification and Context Unification with Tree-Regular Constraints [chapter]

Jordi Levy, Mateu Villaret
2000 Lecture Notes in Computer Science  
Linear Second-Order Uni cation and Context Uni cation are closely related problems. However, their equivalence was never formally proved.  ...  We comment on the possibility that linear second-order uni cation is decidable, if context uni cation is, and how to get rid of the tree-regular constraints.  ...  Bonet and all the anonymous referees for their helpful comments on the paper.  ... 
doi:10.1007/10721975_11 fatcat:sjdoatbovvafhj2rgbm5kqv5z4

Optimizing Higher-Order Pattern Unification [chapter]

Brigitte Pientka, Frank Pfenning
2003 Lecture Notes in Computer Science  
The presented modal framework explains a number of features of the current implementation of higher-order unification in Twelf and provides insight into several optimizations.  ...  This allows us to justify optimizations to pattern unification such as linearization, which eliminates many unnecessary occurs-checks.  ...  The main efficiency problem in pattern unification lies in treating this last case. In particular, we must traverse the term M .  ... 
doi:10.1007/978-3-540-45085-6_40 fatcat:t3c2cnvthrd7zfggww3kxrfsle
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