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## One-context Unification with STG-Compressed Terms is in NP (2012)

Citations: | 3 - 0 self |

### Citations

295 | Unification theory
- Baader, Siekmann
- 1993
(Show Context)
Citation Context ...dentifier 10.4230/LIPIcs.RTA.2012.149 Category Regular Research Paper 1 Introduction Term unification is a basic operation in many areas of computer science, especially in those related to logic (see =-=[1]-=- for a survey). Unifying two terms s, t corresponds to find a substitution σ for the variables occurring in the equation s . = t such that σ(s) = σ(t) holds. The particular case when one of the terms ... |

146 |
The undecidability of the second-order unification problem
- Goldfarb
- 1981
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Citation Context ...s Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany150 which is a particular case of second-order unification. While second-order unification is known to be undecidable =-=[8]-=-, decidability of context unification is still open. However, some interesting results have been found for more particular cases with application in computational linguistics [10, 4, 12]. One-context ... |

92 | Towards a Declarative Query and Transformation Language for XML and Semistructured Data: Simulation Unification
- Bry, Schaffert
- 2002
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Citation Context ...nstances of s within t. In the context of XML processing, combinations of unificaton modulo commutativity and context unification are used for querying XML documents with a logic programming approach =-=[2]-=-. Other relevant variants of unification are related to term compression. Some applications dealing with trees, especially in the context of XML processing, require some kind of succint representation... |

62 | Fully-functional succinct trees.
- Sadakane, Navarro
- 2010
(Show Context)
Citation Context ... kind of succint representation for terms. For this reason, in addition to the well-known Directed Acyclic Graph representation (DAG), several compressed in-memory representations have been developed =-=[18, 15]-=-. Grammar-based compression techniques were initially applied to words [17] and led to important results in string processing. Besides its direct applications in data compression, this kind of represe... |

60 |
Testing equivalence of morphisms on context-free languages
- Plandowski
- 1994
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Citation Context ...well-known Directed Acyclic Graph representation (DAG), several compressed in-memory representations have been developed [18, 15]. Grammar-based compression techniques were initially applied to words =-=[17]-=- and led to important results in string processing. Besides its direct applications in data compression, this kind of representations has also been useful as a technique for complexity analysis [11]. ... |

50 | Efficient memory representation of XML document trees
- Busatto, Lohrey, et al.
- 2008
(Show Context)
Citation Context ...irect applications in data compression, this kind of representations has also been useful as a technique for complexity analysis [11]. This compression mechanisms were extended from words to terms in =-=[3]-=- to introduce Singleton Tree Grammars (STG’s), which allow to represent terms with exponential size and height in linear space. STG’s are useful in the context of XML tree structure compression [15], ... |

32 | Processing compressed texts: A tractability border
- Lifshits
- 2007
(Show Context)
Citation Context ...rm/context. A remarkable result used in the present paper is stated in the following lemma. The rest of known results on STG’s needed in this work are presented in the following section. ◮ Lemma 2.2 (=-=[13, 3]-=-). Given an STG G and two term nonterminals T1, T2 of G, it is decidable in time O(|G| 3 ) whether wG,T1 = wG,T2 . 2.3 Context Unification Given two terms s, t ∈ T (F, V), the context unification prob... |

28 | Computing procedure summaries for interprocedural analysis
- Gulwani, Tiwari
- 2007
(Show Context)
Citation Context ...be solved in nondeterministic polynomial time [6] but it is not known whether it is NP-hard. One of the motivations for this specific variant is its close relation to interprocedural program analysis =-=[9]-=-. The goal of this kind of analysis is to compute all simple invariants of imperative procedural programs. Other interesting applications of one-context unification and matching arise in searching/ext... |

20 |
The complexity of tree automata and XPath on grammarcompressed trees
- Lohrey, Maneth
(Show Context)
Citation Context ...ee Grammars (STG’s), which allow to represent terms with exponential size and height in linear space. STG’s are useful in the context of XML tree structure compression [15], tree automata [16], XPATH =-=[14]-=-, and unification theory [12]. Moreover, polynomial time algorithms for first-order unification and matching for the case when the input is compressed using STG’s have been developed and implemented [... |

15 | On the decidability of context unification
- Levy, Villaret
- 2000
(Show Context)
Citation Context ...own to be undecidable [8], decidability of context unification is still open. However, some interesting results have been found for more particular cases with application in computational linguistics =-=[10, 4, 12]-=-. One-context unification is the particular case when only one context variable, possibly with many occurrences, may appear in the input terms. This problem can be solved in nondeterministic polynomia... |

12 | Context matching for compressed terms
- Gascón, Godoy, et al.
- 2008
(Show Context)
Citation Context ...], and unification theory [12]. Moreover, polynomial time algorithms for first-order unification and matching for the case when the input is compressed using STG’s have been developed and implemented =-=[5, 7]-=-. In this work we extend the result in [6] proving that one-context unification can be solved in nondeterministic polynomial time even in an STG-compressed setting. 2 Preliminaries 2.1 Terms, Contexts... |

10 | Tree structure compression with repair.
- Lohrey, Maneth, et al.
- 2011
(Show Context)
Citation Context ... kind of succint representation for terms. For this reason, in addition to the well-known Directed Acyclic Graph representation (DAG), several compressed in-memory representations have been developed =-=[18, 15]-=-. Grammar-based compression techniques were initially applied to words [17] and led to important results in string processing. Besides its direct applications in data compression, this kind of represe... |

9 | Parameter reduction in grammarcompressed trees
- Lohrey, Maneth, et al.
- 2009
(Show Context)
Citation Context ...Singleton Tree Grammars (STG’s), which allow to represent terms with exponential size and height in linear space. STG’s are useful in the context of XML tree structure compression [15], tree automata =-=[16]-=-, XPATH [14], and unification theory [12]. Moreover, polynomial time algorithms for first-order unification and matching for the case when the input is compressed using STG’s have been developed and i... |

6 | Dominance constraints in stratified context unification
- Erk, Niehren
(Show Context)
Citation Context ...own to be undecidable [8], decidability of context unification is still open. However, some interesting results have been found for more particular cases with application in computational linguistics =-=[10, 4, 12]-=-. One-context unification is the particular case when only one context variable, possibly with many occurrences, may appear in the input terms. This problem can be solved in nondeterministic polynomia... |

6 |
Context Unification with One Context Variable
- Gascón, Godoy, et al.
- 2009
(Show Context)
Citation Context ...h that wG ′ ,C = (t|p1[•]p2) e and |G ′ | ≤ |G| + 2|G|(2|G| + 3) + ⌈log 2(e)⌉ + 1. 3.2 Uncompressed One-Context Unification Consider an instance 〈∆, X , F 〉 of the one-context unification problem. In =-=[6]-=- it is proven that this problem is in NP when the terms in ∆ are represented explicitly. The proposed algorithm is presented as an inference system that modifies the set of equations until a contradic... |

6 | The complexity of monadic second-order unification.
- Levy, Schmidt-Schauß, et al.
- 2008
(Show Context)
Citation Context ...s [17] and led to important results in string processing. Besides its direct applications in data compression, this kind of representations has also been useful as a technique for complexity analysis =-=[11]-=-. This compression mechanisms were extended from words to terms in [3] to introduce Singleton Tree Grammars (STG’s), which allow to represent terms with exponential size and height in linear space. ST... |

6 | On the complexity of bounded second-order unification and stratified context unification
- Levy, Schmidt-Schauß, et al.
(Show Context)
Citation Context ...own to be undecidable [8], decidability of context unification is still open. However, some interesting results have been found for more particular cases with application in computational linguistics =-=[10, 4, 12]-=-. One-context unification is the particular case when only one context variable, possibly with many occurrences, may appear in the input terms. This problem can be solved in nondeterministic polynomia... |

3 | Pattern matching of compressed terms and contexts and polynomial rewriting. Frank report 43, Institut für Informatik. Goethe-Universität Frankfurt am Main
- Schmidt-Schauß
- 2011
(Show Context)
Citation Context ...ations in term rewriting and querying XML-databases: solving an equation F (s) . = t where t is ground and s does not contain the context variable F but may contain first-order variables. As shown in =-=[19]-=-, this problem can be solved in polynomial time when the representation of s is noncompressing. However, it is still open whether the general case is NP-hard or it can be solved in polynomial time. R ... |

2 | First-order unification on compressed terms
- Gascón, Maneth, et al.
- 2011
(Show Context)
Citation Context ...], and unification theory [12]. Moreover, polynomial time algorithms for first-order unification and matching for the case when the input is compressed using STG’s have been developed and implemented =-=[5, 7]-=-. In this work we extend the result in [6] proving that one-context unification can be solved in nondeterministic polynomial time even in an STG-compressed setting. 2 Preliminaries 2.1 Terms, Contexts... |