## Feature Automata and Recognizable Sets of Feature Trees (1993)

Venue: | In TAPSOFT'93, pages 356--375. Springer-Verlag LNCS 668 |

Citations: | 15 - 3 self |

### BibTeX

@INPROCEEDINGS{Niehren93featureautomata,

author = {Joachim Niehren and Andreas Podelski},

title = {Feature Automata and Recognizable Sets of Feature Trees},

booktitle = {In TAPSOFT'93, pages 356--375. Springer-Verlag LNCS 668},

year = {1993},

pages = {356--375},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

Feature trees generalize first-order trees whereby argument positions become keywords ("features") from an infinite symbol set F . Constructor symbols can occur with any argument positions, in any finite number. Feature trees are used to model flexible records; the assumption on the infiniteness of F accounts for dynamic record field updates.

### Citations

235 |
Tree Automata. Akadémiai Kiadó
- Gécseg, Steinby
- 1984
(Show Context)
Citation Context ... corresponds to the characterization by congruence relations, and Theorem 4.1 covers the case of feature trees of depths1, the proof can be done following the standard one for first-order trees (cf., =-=[GS84]-=-). 2 10 7 Conclusion and Further Work The results of this paper together present a complete regular theory of feature trees. They offer a solution to the concrete practical problem of computing with t... |

207 | The monadic second-order logic of graphs. I. Recognizable sets of finite graphs - Courcelle - 1990 |

169 | Tree acceptors and some of their applications - Doner - 1970 |

161 | Generalized finite automata theory with application to a decision problem of second-order logic - Thatcher, Wright |

136 |
Complete Axiomatizations of the Algebras of Finite, Rational and Infinite Trees
- Maher
- 1988
(Show Context)
Citation Context ... framework is provided by universal algebra in the case of first-order trees. Formally, these are the elements of the free algebra over a given signature of function symbols (finite or infinite, cf., =-=[Mah88]). This fr-=-amework yields immediately a "good" notion of automata. In fact, as Courcelle has shown in [Cou89, Cou92], universal algebra provides a framework for a rich variety of trees. Clearly, it is ... |

123 | Towards a meaning of LIFE
- Ait-Kaci, Podelski
- 1991
(Show Context)
Citation Context ...xible feature trees an interesting potential. Precisely, feature trees model record structures. They form the semantics of record calculi like [AK86], which are used in symbolic programming languages =-=[AKP91b]-=- and in computational linguistics (cf., the book [Car92]). In the logical framework for record structures of [BS92], they constitute the interpretation of a completely axiomatizable, and hence decidab... |

95 | Records for logic programming
- Smolka, Treinen
- 1994
(Show Context)
Citation Context ...uctor symbols can label a node with any features attached to it, in any, though finite, number. Although thoroughly investigated [AK86, Smo92, BS92, AKPS92], also in comparison with first-order trees =-=[ST92]-=-, feature trees have never been characterized as composable elements in an algebraic structure, i.e., with operations defined on them. Also, up to now, there has been no corresponding notion of automa... |

83 | Feature Constraint Logics for Unification Grammars, IWBS Report 93
- Smolka
- 1989
(Show Context)
Citation Context ...nstraint C(x) j Sx holds for the multitree x if the root of x is labeled by some symbol in S. Some important feature constraints can be expressed by our new constraints. For example, in the syntax of =-=[Smo92], for F ` F finite, for f-=- 2 F , and for A 2 S: xF ("for exactly the features f in F there exists one edge labeled f from the root"), xf # ("there exists no edge labeled f from the root"), and Ax ("the... |

69 | A feature-based constraint system for logic programming with entailment
- Aït-Kaci, Podelski, et al.
- 1994
(Show Context)
Citation Context ...es. It turns out that this semantical point of view has advantages in efficiency as well. Namely, the correctness of the algorithms for entailment and for solving negated constraints on feature trees =-=[AKPS92]-=- relies on the infiniteness of F . The Method. The first step in solving the problem described above is to build an appropriate algebraic framework. Such a framework is provided by universal algebra i... |

55 |
An algebraic semantics approach to the effective resolution of type equations
- Ait-Kaci
- 1986
(Show Context)
Citation Context ...ing languages like Prolog and ML, this gives the more flexible feature trees an interesting potential. Precisely, feature trees model record structures. They form the semantics of record calculi like =-=[AK86]-=-, which are used in symbolic programming languages [AKP91b] and in computational linguistics (cf., the book [Car92]). In the logical framework for record structures of [BS92], they constitute the inte... |

33 |
The Logic of Typed Feature Structures, volume 32 of Cambridge Tracts in Theoretical
- Carpenter
- 1992
(Show Context)
Citation Context ...feature trees model record structures. They form the semantics of record calculi like [AK86], which are used in symbolic programming languages [AKP91b] and in computational linguistics (cf., the book =-=[Car92]-=-). In the logical framework for record structures of [BS92], they constitute the interpretation of a completely axiomatizable, and hence decidable, first-order theory. partially supported by Graduiert... |

33 | Equational formulae with membership constraints
- Comon, Delor
- 1994
(Show Context)
Citation Context ...t for circular data structures, like, e.g., circular lists, it is necessary to consider infinite (rational) feature trees. Thus, it would be useful to construct a regular theory of these. Finally, in =-=[CD91]-=- it is shown that the first-order theory of a tree automaton is decidable (in the case of a finite signature). More precisely, it is possible to solve first-order formulas built up from equalities bet... |

27 | A complete and recursive feature theory
- Backofen, Smolka
- 1995
(Show Context)
Citation Context ...cs of record calculi like [AK86], which are used in symbolic programming languages [AKP91b] and in computational linguistics (cf., the book [Car92]). In the logical framework for record structures of =-=[BS92]-=-, they constitute the interpretation of a completely axiomatizable, and hence decidable, first-order theory. partially supported by Graduierten-Kolleg Informatik der Universitat des Saarlandes. 1 As g... |

20 |
On recognizable sets and tree-automata
- Courcelle
- 1989
(Show Context)
Citation Context ...esults, together with the previous ones, are necessary to present a complete regular theory of feature trees and to offer a solution to the practical problem 2 The unranked unordered trees studied in =-=[Cou89]-=- (the number of arguments of the nodes is not restricted, and the arguments are not ordered) are a special case of multitrees, namely with just one feature. In the framework of [Cou89], however, recog... |

20 |
Set values for unification-based grammar formalisms and logic programming
- Rounds
- 1988
(Show Context)
Citation Context ...ree species, also those considered in [Cou89, Cou92]) 2 symbols. We call these multitrees. 2 Multitrees are of interest on their own, namely for representation of knowledge with set-valued attributes =-=[Rou88]. Thus, fe-=-ature trees are multitrees with the restriction that features are "functional," i.e., all edges outgoing from the same node are labeled with different features. Feature automata recognize la... |

5 |
Recognizable sets of unrooted trees
- Courcelle
- 1992
(Show Context)
Citation Context ...introduce feature trees and the more general multitrees as elements of an algebra that we define, called J . This yields the notion of a J -automaton. This section follows the approach of [Cou89] and =-=[Cou92]-=-. In the following we will assume a given set S of constructor symbols (also called sorts, referred to by A, B, etc.) and a given set F of feature symbols (also called attributes, or record field sele... |

5 |
Elements of a theory of tree codes
- Nivat
- 1992
(Show Context)
Citation Context ..., the operation composing feature trees in the algebra takes a record value and adds a record field containing another value to it. In a special case, this amounts to Nivat's notion of `sum of trees' =-=[Niv92]-=-; thus, incidentally, we obtain an algebraic formalization hereof. To define feature automata as algebras, it is useful to consider the class of all finite trees whose nodes are labeled by constructor... |

3 |
Set Constraints: A
- Pacholski, Podelski
- 1997
(Show Context)
Citation Context ...such as LIFE [AKP91b], we need to compute efficiently the intersection of two types (roughly, for unification). Concurrent systems, in connection with control mechanisms such as residuation or guards =-=[AKP91a]-=-, require furthermore an efficient test of the subset relation (matching). Thus, we need to provide a formalism defining the types in a way which is expressive enough and yet keeps the two problems de... |

3 |
Automata, Language and Machine, volume A of Applied and Pure Mathematics
- Eilenberg
- 1974
(Show Context)
Citation Context ...aints and Mrecognizability coincide. The main idea is that the mapping: x 7! cardf(f; A) 2 x j f 2 F; A 2 Tg is essentially a homomorphism from M into N . 2 We finish this section noting a fact (cf., =-=[Eil74]-=-) which expresses exactly that feature automata can count features either threshold or modulo a natural number. Fact 4.2 A language of natural numbers is recognizable iff it can be decomposed into a f... |