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Weighted tree automata and weighted logics

Manfred Droste, Heiko Vogler
2006 Theoretical Computer Science  
This generalizes corresponding classical results of Thatcher, Wright, and Doner for tree languages and it extends recent results of Droste and Gastin [Weighted automata and weighted logics, informal power  ...  We prove that a restricted version of this logic characterizes the class of formal tree series which are accepted by weighted bottom-up finite state tree automata.  ...  In this paper, we will consider a weighted logic for trees and we will achieve an extension of the result of Thatcher and Wright [39] and Doner [16] to the case of weighted tree automata.  ... 
doi:10.1016/j.tcs.2006.08.025 fatcat:ojp2unszfngltixhakm5uvjoty

Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics [chapter]

Manfred Droste, Doreen Götze, Steffen Märcker, Ingmar Meinecke
2011 Lecture Notes in Computer Science  
We establish a characterization of the behaviors of these weighted finite tree automata by fragments of weighted monadic second-order logic.  ...  For bi-locally finite bimonoids, we show that weighted tree automata capture the expressive power of several semantics of full weighted MSO logic. Decision procedures follow as consequences.  ...  Here, we present another concept of weighted tree automata and their characterization by weighted logics.  ... 
doi:10.1007/978-3-642-24897-9_2 fatcat:4n5wn54jajbw7idpl4irzs6w34

Weighted versus Probabilistic Logics [chapter]

Benedikt Bollig, Paul Gastin
2009 Lecture Notes in Computer Science  
While a mature theory around logics such as MSO, LTL, and CTL has been developed in the pure boolean setting of finite automata, weighted automata lack such a natural connection with (temporal) logic and  ...  We establish expressiveness results on our logics giving translations from weighted and probabilistic CTL into weighted MSO. ⋆ Partially supported by projects ARCUSÎle de France-Inde and ANR-06-SETIN-003  ...  We then defined wCTL and wCTL * over weighted trees and gave transformations of these logics into wMSO.  ... 
doi:10.1007/978-3-642-02737-6_2 fatcat:vrvjbgt43rfrdl6ccgo6dqfwo4

A unifying survey on weighted logics and weighted automata

Paul Gastin, Benjamin Monmege
2015 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
We show at the level of the abstract semantics that weighted automata and core weighted logic have the same expressive power.  ...  Logical formalisms equivalent to weighted automata have been the topic of numerous research papers in the recent years.  ...  However, these additional conditions are not necessary to define the semantics of weighted automata and to obtain the equivalence between weighted automata and our weighted logic that will be presented  ... 
doi:10.1007/s00500-015-1952-6 fatcat:mnmhjetoyfb6hj443mdx6vaz2a

Weighted Automata and Logics on Graphs [chapter]

Manfred Droste, Stefan Dück
2015 Lecture Notes in Computer Science  
As a consequence, we obtain corresponding Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words.  ...  Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words.  ...  We showed that weighted word, tree, picture, or nested word automata are special instances of these general weighted graph automata, which gives us results of [9] , [14] , [17] , and [24] as corollaries  ... 
doi:10.1007/978-3-662-48057-1_15 fatcat:d53kbssbsbhozbxyh6yhxjc6cy

A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings

Gustav Grabolle
2021 Electronic Proceedings in Theoretical Computer Science  
We give a logical characterization of weighted alternating automata, which uses weighted MSO logic for trees.  ...  To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree automata (WFTA) and a specific class of tree homomorphism.  ...  This will lead us directly into a logical characterization of quantitative languages recognized by weighted alternating automata with the help of weighted restricted MSO logic for weighted tree automata  ... 
doi:10.4204/eptcs.346.16 fatcat:kt53rrkfuvdvtokr7ca54cunxq

On Finite and Polynomial Ambiguity of Weighted Tree Automata [chapter]

Erik Paul
2016 Lecture Notes in Computer Science  
We consider finite and polynomial ambiguity of weighted tree automata.  ...  We also outline how these results can be used to capture the ambiguity of weighted tree automata with weighted logics.  ...  I would like to thank Professor Manfred Droste, Peter Leupold and Vitaly Perevoshchikov for helpful discussions and suggestions.  ... 
doi:10.1007/978-3-662-53132-7_30 fatcat:saymhopdqfd3rawjrty4mgc7j4

Reasoning with Prototypes in the Description Logic $${\mathcal {ALC}}$$ ALC Using Weighted Tree Automata [chapter]

Franz Baader, Andreas Ecke
2016 Lecture Notes in Computer Science  
We show how weighted alternating parity tree automata (wapta) over the non-negative integers can be used to define pdfs, and how this allows us to use both concepts and pointed interpretations as prototypes  ...  We introduce an extension to Description Logics that allows us to use prototypes to define concepts.  ...  As explained before, we will use weighted alternating tree automata to define pdfs.  ... 
doi:10.1007/978-3-319-30000-9_5 fatcat:3gw733yzbbennjvf22fn62c7fa

Quantitative Verification of Weighted Kripke Structures [chapter]

Patricia Bouyer, Patrick Gardy, Nicolas Markey
2014 Lecture Notes in Computer Science  
Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight  ...  We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.  ...  Weighted temporal logics We extend both branching-time temporal logic CTL [CE82,QS82] and linear-time temporal logic LTL [Pnu77] with numerical constraints on weights: Definition 2.  ... 
doi:10.1007/978-3-319-11936-6_6 fatcat:fc3xuqmwrzhibpau7ijyjqxrry

Weighted automata with storage

Luisa Herrmann, Heiko Vogler, Manfred Droste
2019 Information and Computation  
In its turn, these logics are based on the weighted MSO logic in [DG05, DG07] for weighted string automata and [DV06] for weighted tree automata over commutative semirings.  ...  For a comparison of the logic from this chapter with our logic for weighted tree automata with storage in Chapter 3 we refer to Section 3.3.2.  ...  Moreover, we provided a logical characterization of the languages recognized by weighted symbolic automata with data storage.  ... 
doi:10.1016/j.ic.2019.104447 fatcat:ipq7xamnlveujkl3raxdl72fvi

Curriculum Vitae of Zoltán Ésik

2017 Acta Cybernetica  
Other conference and seminar presentations Talks at cca. 80 international conferences and workshops.  ...  Seminar and/or colloquium presentations at the following universities and research centers (several talks at some places):  ...  Weighted Automata: Theory and Applications, Leipzig, 2014. Automata, Logic, Formal languages and Algebra, Stellenbosch, 2013. Mathematics and Informatics, Targu Mures, 2013.  ... 
doi:10.14232/actacyb.23.1.2017.22 fatcat:23vz5jef6rflzftjmtlztnxsoa

Weighted Automata and Logics on Infinite Graphs [chapter]

Stefan Dück
2016 Lecture Notes in Computer Science  
We show a Büchi-like connection between graph automata and logics for infinite graphs.  ...  This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting.  ...  Acknowledgments: I want to thank Manfred Droste and Tobias Weihrauch for helpful discussions and insightful remarks on earlier drafts of this paper.  ... 
doi:10.1007/978-3-662-53132-7_13 fatcat:jkr7qckpq5fnnk53qf26mybqgy

Preface of STACS 2013 Special Issue

Anca Muscholl, Martin Dietzfelbinger
2015 Theory of Computing Systems  
temporal logic EF, and languages definable among all trees in weak MSO logic.  ...  Regular languages of infinite trees have been thoroughly investigated in logic and automata theory since the founding work by Rabin and Büchi, but a general algebraic formalism is still missing.  ... 
doi:10.1007/s00224-015-9654-0 fatcat:caqkhdumvnduvgflvjdzg4qq4q

Weighted Logics for Unranked Tree Automata

Manfred Droste, Heiko Vogler
2009 Theory of Computing Systems  
We define a weighted monadic second order logic for unranked trees and the concept of weighted unranked tree automata, and we investigate the expressive power of these two concepts.  ...  We show that weighted tree automata and a syntactically restricted weighted MSO-logic have the same expressive power in case the semiring is commutative or in case we deal only with ranked trees, but,  ...  As an automata-theoretic counterpart of our weighted MSO-logic, we will introduce weighted tree automata over unranked trees (for short: wta) where the weights are taken from a semiring S.  ... 
doi:10.1007/s00224-009-9224-4 fatcat:th7wikdswra6fj4acvhyfw2jle

Weak MSO+U with Path Quantifiers over Infinite Trees [chapter]

Mikołaj Bojańczyk
2014 Lecture Notes in Computer Science  
This paper presents a logic over infinite trees with decidable satisfiability. The logic is weak monadic second-order logic with U and path quantifiers (wmso+up).  ...  This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths.  ...  I would like to thank Szymon Toruńczyk and Martin Zimmermann for months of discussions about this paper; in particular Szymon Toruńczyk suggested the use of profinite trees.  ... 
doi:10.1007/978-3-662-43951-7_4 fatcat:fg7cwa6t2vgttdan4wtvs4wvs4
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