Results 1  10
of
10
On the Minimization of XML Schemas and Tree Automata for Unranked Trees
, 2006
"... Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. First, we study unranked tree automata that are standard in database theory, assuming bottomup determinism and that horizontal recursion is re ..."
Abstract

Cited by 31 (9 self)
 Add to MetaCart
(Show Context)
Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. First, we study unranked tree automata that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal automata in that class are not unique and that minimization is npcomplete. Second, we study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottomup deterministic stepwise tree automata yield the most succinct representations. Third, we investigate abstractions of XML schema languages. In particular, we show that the class of onepass preorder typeable schemas allows for polynomial time minimization and unique minimal models.
Bisimulation Minimisation for Weighted Tree Automata
, 2007
"... We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings t ..."
Abstract

Cited by 9 (6 self)
 Add to MetaCart
We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings the time complexity is slightly higher (linear instead of logarithmic in the number of states). We discuss implementations of these algorithms on a typical task in natural language processing.
YakYak: Parsing with Logical Side Constraints
 In Proceedings of DLT'99
, 1999
"... Programming language syntax is often described by means of a contextfree grammar, which is restricted by constraints programmed into the action code associated with productions. Without such code, the grammar would explode in size if it were to describe the same language. We present the tool Ya ..."
Abstract

Cited by 7 (7 self)
 Add to MetaCart
(Show Context)
Programming language syntax is often described by means of a contextfree grammar, which is restricted by constraints programmed into the action code associated with productions. Without such code, the grammar would explode in size if it were to describe the same language. We present the tool YakYak, which extends Yacc with rstorder logic for specifying constraints that are regular tree languages. Concise formulas about the parse tree replace explicit programming, and they are turned into canonical attribute grammars through tree automata calculations. YakYak is implemented as a preprocessor for Yacc, in which the transitions of the calculated tree automata are merged into the action code. We provide both practical experience and theoretical evidence that the YakYak approach results in fast and concisely specied parsers. 1 Introduction We introduce a declarative notation, a rstorder logic on trees, to specify ecient parsers that require fewer attributes and less explic...
Minimizing Deterministic Weighted Tree Automata
, 2008
"... The problem of efficiently minimizing deterministic weighted tree automata (wta) is investigated. Such automata have found promising applications as language models in Natural Language Processing. A polynomialtime algorithm is presented that given a deterministic wta over a commutative semifield, o ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
The problem of efficiently minimizing deterministic weighted tree automata (wta) is investigated. Such automata have found promising applications as language models in Natural Language Processing. A polynomialtime algorithm is presented that given a deterministic wta over a commutative semifield, of which all operations including the computation of the inverses are polynomial, constructs an equivalent minimal (with respect to the number of states) deterministic and total wta. If the semifield operations can be performed in constant time, then the algorithm runs in time O(rmn 4) where r is the maximal rank of the input symbols, m is the number of transitions, and n is the number of states of the input wta.
Partial automata and finitely generated congruences: an extension of Nerode’s theorem
 Proc. Conf. Logical Methods in Math. and Comp. Sci
, 1992
"... For Anil Nerode, on the occasion of his 60 th birthday ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
For Anil Nerode, on the occasion of his 60 th birthday
MyhillNerode theorem for recognizable tree series revisited
, 2007
"... In this contribution the MyhillNerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zerodivisor free and commutative semiring, then the MyhillNerode congruence ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
In this contribution the MyhillNerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zerodivisor free and commutative semiring, then the MyhillNerode congruence relation has nite index. By [Borchardt: MyhillNerode Theorem for Recognizable Tree Series. LNCS 2710. Springer 2003] the converse holds for commutative semi elds, but not in general. In the second part, a slightly adapted version of the MyhillNerode congruence relation is de ned and a characterization is obtained for allaccepting weighted tree automata over multiplicatively cancellative and commutative semirings.
Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences?
"... Abstract. Fix an integer h ≥ 1. In the universe of coloured trees of height at most h, we prove that for any MSO formula with r variables there exists a set of kernels, each of size bounded by an elementary function of r and the number of colours. This yields two noteworthy consequences. Consider ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Fix an integer h ≥ 1. In the universe of coloured trees of height at most h, we prove that for any MSO formula with r variables there exists a set of kernels, each of size bounded by an elementary function of r and the number of colours. This yields two noteworthy consequences. Consider any graph class G having a simple MSO interpretation in the universe of coloured trees of height h (equivalently, G is a class of shrubdepth h). First, G admits an MSO model checking algorithm whose runtime has an elementary dependence on the formula size. Second, on G the expressive powers of FO and MSO coincide (which extends a 2012 result of Elberfeld, Grohe, and Tantau [9]).
Cut Sets as Recognizable Tree Languages
"... A tree series over a semiring with partially ordered carrier set can be considered as a fuzzy set. We investigate conditions under which it can also be understood as a fuzzi ed recognizable tree language. In this sense, su cient conditions are presented which, when imposed, ensure that every cut set ..."
Abstract
 Add to MetaCart
A tree series over a semiring with partially ordered carrier set can be considered as a fuzzy set. We investigate conditions under which it can also be understood as a fuzzi ed recognizable tree language. In this sense, su cient conditions are presented which, when imposed, ensure that every cut set, i.e., the preimage of a prime lter of the carrier set, is a recognizable tree language. Moreover, such conditions are also presented for cut sets of recognizable tree series. 1
MyhillNerode Theorem for Sequential Transducers over Unique GCDMonoids
"... Abstract. We generalize the classical MyhillNerode theorem for finite automata to the setting of sequential transducers over unique GCDmonoids, which are cancellative monoids in which every two nonzero elements admit a unique greatest common (left) divisor. We prove that a given formal power serie ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We generalize the classical MyhillNerode theorem for finite automata to the setting of sequential transducers over unique GCDmonoids, which are cancellative monoids in which every two nonzero elements admit a unique greatest common (left) divisor. We prove that a given formal power series is sequential, if and only if it is directed and our MyhillNerode equivalence relation has finite index. As in the classical case, our MyhillNerode equivalence relation also admits the construction of a minimal (with respect to the number of states) sequential transducer recognizing the given formal power series. Deterministic finite automata and sequential transducers are applied, for example, in lexical analysis, digital image manipulation, and speech processing [2]. In the latter application area also very large sequential transducers, i.e., transducers having several million states, over various monoids are encountered [2], so without minimization algorithms [4] the applicability of sequential transducers would be severely hampered. In [2, 3] efficient algorithms for the minimization of sequential transducers are presented in case the weight is taken out of the monoid ( ∆ ∗ , ·, ε) or out of the monoid (IR +, +, 0). A MyhillNerode theorem also allowing minimization is wellknown for sequential transducers over groups [1]. We use (A, ⊙, 1, 0) to denote a monoid with the absorbing element 0. A unique GCDmonoid is a cancellation monoid (A, ⊙, 1, 0) in which (i) a1 implies a = 1, (ii) a greatest common divisor (gcd) exists for every two nonzero elements, and (iii) a least common multiple (lcm) exists for every two nonzero elements having a common multiple. Unique GCDmonoids exist in abundance (e.g., (IN ∪ {∞}, +, 0, ∞) and (IN, ·, 1, 0) as well as the monoids mentioned in the previous paragraph).