A Weighted MSO Logic with Storage Behaviour and Its Büchi-Elgot-Trakhtenbrot Theorem

Vogler, Heiko; Droste, Manfred; Herrmann, Luisa

doi:10.1007/978-3-319-30000-9_10

Cited by 10 publications

(18 citation statements)

References 17 publications

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“…Each formula, called expression, of this logic is interpreted over finite, labeled, and ordered trees. Our new weighted MSO-logic generalizes (i) the weighted MSO-logic with storage behaviour of [VDH16] by considering trees as models, and (ii) M-expressions of [FSV12,FV18] by adding storage type. Our Büchi-Elgot-Trakhtenbrot theorem states that weighted tree languages generated by (S, Σ, K)-rtg are the same as weighted tree languages definable by expressions.…”

Section: B üChi-elgot-trakhtenbrot Theoremmentioning

confidence: 99%

“…In automata theory, weighted string automata with storage are a very recent topic of research [HV15,HV16,VDH16]. This model generalizes finite-state string automata in two directions.…”

Section: Introductionmentioning

confidence: 99%

“…In [DV13,DV14] weighted pushdown automata were investigated where the weights are taken from a unital valuation monoid. The automata studied in [HV15,VDH16] are weighted string automata with arbitrary storage in which the weights are taken from unital valuation monoids. In [HV16] weighted symbolic automata with data storage were introduced, which cover weighted string automata with storage and, e.g., weighted visibly pushdown automata and weighted timed automata.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 7 we prove a characterization of (S, Σ, K)-regular tree languages in terms of weighted monadic second order logic (MSO). For this, we introduce a weighted MSO-logic with storage behaviour based on M-expressions of [FSV12,FV18] and on the MSO-logic introduced in [VDH16]. However, our new logic generalizes the weighted MSO-logic with storage behaviour of [VDH16] by considering trees as models and by allowing chain rules.…”

Section: Introductionmentioning

confidence: 99%

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Weighted Regular Tree Grammars with Storage

Fülöp,

Herrmann,

Vogler

2017

Preprint

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We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a weighted tree language, which is a mapping from the set of trees to the multioperator monoid. We prove that, for multioperator monoids canonically associated to particular strong bimonoids, the support of the generated weighted tree languages can be generated by (unweighted) regular tree grammars with storage. We characterize the class of all generated weighted tree languages by the composition of three basic concepts. Moreover, we prove results on the elimination of chain rules and of finite storage types, and we characterize weighted regular tree grammars with storage by a new weighted MSO-logic.

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Section: B üChi-elgot-trakhtenbrot Theoremmentioning

confidence: 99%

“…In automata theory, weighted string automata with storage are a very recent topic of research [HV15,HV16,VDH16]. This model generalizes finite-state string automata in two directions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weighted Regular Tree Grammars with Storage

Fülöp,

Herrmann,

Vogler

2017

Preprint

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“…It is well-known [TW68] that tree automata are as expressive as monadic second-order logic with two successors. This celebrated result was recently generalized to the weighted setting for various weight structures [DV06,Man08,DGMM11,VDH16], so quantitative specifications are readily available. However, one of the main insights gained in the development of the mona toolkit [KM01] (or the spass system [WDF + 09]) was that the transformation of a formula into an equivalent tree automaton heavily relies on the minimization of the constructed deterministic tree automata as the automata otherwise grow far too quickly.…”

Section: Introductionmentioning

confidence: 99%

Pushing for weighted tree automata

Hanneforth¹,

Maletti²,

Quernheim³

2018

Logical Methods in Computer Science ; Volume 14

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A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful for bottom-up deterministic wta, where it can be used for minimization and equivalence testing. In both applications a careful selection of the weights to be redistributed followed by normalization allows a reduction of the general problem to the corresponding problem for bottom-up deterministic unweighted tree automata. This approach was already successfully used by Mohri and Eisner for the minimization of deterministic weighted string automata. Moreover, the new equivalence test for two wta M and M runs in time O (|M | + |M |) log (|Q| + |Q |) , where Q and Q are the states of M and M , respectively, which improves the previously best run-time O |M | • |M | .

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Rational Weighted Tree Languages with Storage and the Kleene-Goldstine Theorem

Fülöp

Vogler

2019

Lecture Notes in Computer Science

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A Weighted MSO Logic with Storage Behaviour and Its Büchi-Elgot-Trakhtenbrot Theorem

Cited by 10 publications

References 17 publications

Weighted Regular Tree Grammars with Storage

Weighted Regular Tree Grammars with Storage

Pushing for weighted tree automata

Rational Weighted Tree Languages with Storage and the Kleene-Goldstine Theorem

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