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Pebble Weighted Automata and Transitive Closure Logics [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2010 Lecture Notes in Computer Science  
weighted automata ◮ Automaton with 2-way mechanism and pebbles {1, . . . , r }  ...  Theorem (Droste & Gastin'05) Weighted automata = wRMSO (effective translation). 9/15 Lemma Pebble weighted automata are stable under wFO constructs.  ...  Definition: Weighted First-order logic where k ∈ K , a ∈ Σ, x, y are first-order variables.  ... 
doi:10.1007/978-3-642-14162-1_49 fatcat:bpzbzioovbctjdnjsdxaqtvwu4

Logical characterization of weighted pebble walking automata

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
In this paper, we establish the expressive power of weighted pebble walking automata in terms of transitive closure logic, lifting a similar result by Engelfriet and Hoogeboom from the Boolean case to  ...  To address this drawback, weighted automata have recently been generalized to weighted pebble walking automata, which proved useful as a tool for the specification and evaluation of quantitative properties  ...  Conclusion We established expressive equivalence of weighted pebble walking automata and weighted first-order logic with transitive closure.  ... 
doi:10.1145/2603088.2603118 dblp:conf/csl/BolligGMZ14 fatcat:xeslb5zytfcxnakqbbyczn7mze

Pebble Weighted Automata and Weighted Logics

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2014 ACM Transactions on Computational Logic  
Our main result states that two-way pebble weighted automata, oneway pebble weighted automata, and our weighted logic are expressively equivalent.  ...  Equipped with pebbles, they go beyond the class of recognizable formal power series: they capture weighted first-order logic enriched with a quantitative version of transitive closure.  ...  ACKNOWLEDGMENTS The authors would like to thank the anonymous referees for their valuable comments that permitted to simplify some proofs, and globally improve the quality of this paper.  ... 
doi:10.1145/2579819 fatcat:2lgcju54lrbmpbvxt6iirj6fwm

Weighted Specifications over Nested Words [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege
2013 Lecture Notes in Computer Science  
The specification formalisms are weighted regular expressions (with forward and backward moves following linear edges or call-return edges), weighted first-order logic, and weighted temporal logics.  ...  We introduce weighted automata walking in nested words, possibly dropping/lifting (reusable) pebbles during the traversal.  ...  This is due to the power of η steps, which gives to wTL a flavor of weighted transitive closure (see [5] ), and of regular LTL [14] .  ... 
doi:10.1007/978-3-642-37075-5_25 fatcat:ft275yydpzb7tobz3oguetgyvm

Adding Pebbles to Weighted Automata [chapter]

Paul Gastin, Benjamin Monmege
2012 Lecture Notes in Computer Science  
We extend weighted automata and weighted rational expressions with 2-way moves and (reusable) pebbles.  ...  We show with examples from natural language modeling and quantitative model-checking that weighted expressions and automata with pebbles are more expressive and allow much more natural and intuitive specifications  ...  Acknowledgements The authors would like to thank Benedikt Bollig and Jacques Sakarovitch for helpful discussions.  ... 
doi:10.1007/978-3-642-31606-7_4 fatcat:e6lk5p6zavfxpi7juwjijeqes4

Quantitative Monadic Second-Order Logic

Stephan Kreutzer, Cristian Riveros
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
We further refine the analysis of this logic and obtain fragments that characterise exactly subclasses of weighted automata defined by the level of ambiguity allowed in the automata.  ...  In this way we obtain a simple logic which is equally expressive to weighted automata.  ...  Finitely ambiguous weighted automata form a sub-class of WA with very good closure properties.  ... 
doi:10.1109/lics.2013.16 dblp:conf/lics/KreutzerR13 fatcat:2mworivl2fhzrgdlybwwmf43aq

Adding pebbles to weighted automata: Easy specification & efficient evaluation

Paul Gastin, Benjamin Monmege
2014 Theoretical Computer Science  
We extend weighted automata and weighted rational expressions with 2-way moves and (reusable) pebbles.  ...  We show with examples from natural language modeling and quantitative model-checking that weighted expressions and automata with pebbles are more expressive and allow much more natural and intuitive specifications  ...  Acknowledgements The authors would like to thank Benedikt Bollig and Jacques Sakarovitch for helpful discussions.  ... 
doi:10.1016/j.tcs.2014.02.034 fatcat:disnlwt3x5drtkzrl34tnljcim

A Probabilistic Kleene Theorem [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2012 Lecture Notes in Computer Science  
Our result actually extends to two-way probabilistic automata with pebbles and corresponding expressions.  ...  We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability.  ...  Just like classical finite automata, weighted automata over semirings enjoy characterizations in terms of monadic second-order logic [13, 6] .  ... 
doi:10.1007/978-3-642-33386-6_31 fatcat:m4lnnln4gngxjmtqnsfs3yblz4

Advanced Automata Minimization [article]

Lorenzo Clemente, Richard Mayr
2012 arXiv   pre-print
This can be used to scale up applications of automata in formal verification tools and decision procedures for logical theories. The algorithm is based on new transition pruning techniques.  ...  We tested our algorithm on Buchi automata derived from LTL-formulae, many classes of random automata and automata derived from mutual exclusion protocols, and compared its performance to the well-known  ...  Direct, delayed, fair and backward k-pebble simulations are not transitive in general, but their transitive closures are GFI preorders; the direct, delayed and backward variants are also GFQ.  ... 
arXiv:1210.6624v1 fatcat:76y7x7dv5be5fobkirgfah7jjm

Advanced automata minimization

Richard Mayr, Lorenzo Clemente
2013 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '13  
Direct, delayed, fair and backward k-pebble simulations are not transitive in general, but their transitive closures are GFI preorders; the direct, delayed and backward variants are also GFQ.  ...  Model checking algorithms and automata-based decision procedures for logical theories compute automata products, unions, complements, projections, etc., and thus the sizes of automata grow rapidly.  ...  k < k transitions.  ... 
doi:10.1145/2429069.2429079 dblp:conf/popl/MayrC13 fatcat:4h3lktk2cvck3ixjm7f2wrpluu

Advanced automata minimization

Richard Mayr, Lorenzo Clemente
2013 SIGPLAN notices  
Direct, delayed, fair and backward k-pebble simulations are not transitive in general, but their transitive closures are GFI preorders; the direct, delayed and backward variants are also GFQ.  ...  Model checking algorithms and automata-based decision procedures for logical theories compute automata products, unions, complements, projections, etc., and thus the sizes of automata grow rapidly.  ...  k < k transitions.  ... 
doi:10.1145/2480359.2429079 fatcat:yratr3f6mba4xogpmhs7cdpgwa

Page 4671 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
The simpler problems are the determination of the transitive closure, the strongly connected components, the weakly connected components or the spanning trees of directed graphs.  ...  Halpern and Jerzy Tiuryn, On the power of nondeterminism in dynamic logic (pp. 48-60); A. Bertoni, G. Mauri and N.  ... 

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.  ...  We also show that a suitable weighted MSO logic is expressively equivalent to weighted graph automata.  ...  Conclusion We introduced a weighted generalization of Thomas' graph acceptors [33, 34] and a suitable weighted logic in the sense of Droste and Gastin [9] .  ... 
doi:10.1007/978-3-662-48057-1_15 fatcat:d53kbssbsbhozbxyh6yhxjc6cy

Register Transducers Are Marble Transducers

Gaëtan Douéneau-Tabot, Emmanuel Filiot, Paul Gastin, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
Our results can be interpreted in terms of program optimization for simple recursive and iterative programs.  ...  Alur and Cerný introduced an equivalent model of transducers with registers called copyless streaming string transducers.  ...  On the other hand, [7] studies in detail a weighted logics which describes the functions computed by weighted automata.  ... 
doi:10.4230/lipics.mfcs.2020.29 dblp:conf/mfcs/Doueneau-TabotF20 fatcat:ufd2taxnlvhvvogm334la3scgq

Page 4231 of Mathematical Reviews Vol. , Issue 81J [page]

1981 Mathematical Reviews  
Savage, Graph pebbling with many free pebbles can be difficult (pp. 326-332); Martin Tompa, Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations (pp  ...  Meyer and Rohit Parikh, Definability in dynamic logic (pp. 1-7); John H.  ... 
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