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Finite Sequentiality of Unambiguous Max-Plus Tree Automata

Erik Paul, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
We show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata.  ...  The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton  ...  In particular, we see that the behavior of a trim unambiguous max-plus-WTA is finitely sequential if it does not satisfy the tree fork property. This concludes the proof of Theorem 5. S TA C S  ... 
doi:10.4230/lipics.stacs.2019.55 dblp:conf/stacs/Paul19 fatcat:nly4wsmz7rggtdyqb6tisndnla

Finite Sequentiality of Unambiguous Max-Plus Tree Automata

Erik Paul
2021 Theory of Computing Systems  
AbstractWe show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata.  ...  The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton  ...  Applications for max-plus tree automata include proving the termination of certain term rewriting systems [24] , and they are also commonly employed in natural language processing [33] in the form of  ... 
doi:10.1007/s00224-020-10021-w fatcat:hrsbcpefyjedjlumlzmc336e6i

Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

Erik Paul, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
We show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring.  ...  The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton  ...  Applications of max-plus tree automata include proving the termination of certain term rewriting systems [24] and they are commonly employed in natural language processing [35] in the form of probabilistic  ... 
doi:10.4230/lipics.icalp.2020.137 dblp:conf/icalp/Paul20 fatcat:asqessv6xfa45bzzmxagg67zl4

Quasi-interpretations a way to control resources

G. Bonfante, J.-Y. Marion, J.-Y. Moyen
2011 Theoretical Computer Science  
By combining the quasi-interpretation method with termination tools (here term orderings), we obtained several characterizations of complexity classes starting from Ptime and Pspace.  ...  a broad class which is relevant for feasible computations.  ...  For this reason, Amadio [1] considered the max-plus algebra over rational numbers.  ... 
doi:10.1016/j.tcs.2011.02.007 fatcat:rbra7ldrz5gole6m7hr4qzygia

Tree compression using string grammars [article]

Moses Ganardi, Danny Hucke, Markus Lohrey, Eric Noeth
2015 arXiv   pre-print
Other problems on tree traversals turn out to be intractable, e.g. pattern matching and evaluation of tree automata.  ...  of a tree, tree navigation, or evaluation of Boolean expressions.  ...  max-plus expressions, and membership for tree automata.  ... 
arXiv:1504.05535v2 fatcat:hvjk3ji4lbdnnllfczbycsjeca

An Automated Approach to the Collatz Conjecture [article]

Emre Yolcu, Scott Aaronson, Marijn J.H. Heule
2021 arXiv   pre-print
Finally, we adapt our rewriting system to show that other open problems in mathematics can also be approached as termination problems for relatively small rewriting systems.  ...  We explore the Collatz conjecture and its variants through the lens of termination of string rewriting.  ...  We thank Jeremy Avigad and Jasmin Blanchette for their detailed comments on an early draft. Finally, we thank anonymous reviewers of CADE for their comments on the conference version of this paper.  ... 
arXiv:2105.14697v1 fatcat:wvxrhfh23ff2rgm4abcmmsfr6u

Weighted automata with storage

Luisa Herrmann, Heiko Vogler, Manfred Droste
2019 Information and Computation  
Let Σ = {a, b}, C = {x}, and consider the max-plus semiring ( ≥0 ∪ {−∞}, max, +, −∞, 0) of non-negative reals.  ...  can be seen as initial storage configurations) into terminal trees in a very similar way as A recognizes trees.  ...  For this, we split π into predicates π (p, f ) for each (p, f ) ∈ Ω and attach the occurrence of p and f in a transition of A ′ to the usage of π (p, f ) . for each π (p, f ) ∈ Π ′ .  ... 
doi:10.1016/j.ic.2019.104447 fatcat:ipq7xamnlveujkl3raxdl72fvi

When is Containment Decidable for Probabilistic Automata? [article]

Laure Daviaud, Marcin Jurdziński, Ranko Lazić, Filip Mazowiecki, Guillermo A. Pérez, James Worrell
2020 arXiv   pre-print
In this paper we provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata.  ...  The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata.  ...  Mazowiecki, by the French National Research Agency (ANR) in the frame of the "Investments for the future" Programme IdEx Bordeaux (ANR-10-IDEX-03-02); G. A. Pérez, by an F.R.S.  ... 
arXiv:1804.09077v4 fatcat:ds5azb7dozfepj6iovjg6wjoxm

Arctic Termination ...Below Zero [chapter]

Adam Koprowski, Johannes Waldmann
Lecture Notes in Computer Science  
We introduce the arctic matrix method for automatically proving termination of term rewriting.  ...  This extends the matrix method for term rewriting and the arctic matrix method for string rewriting.  ...  In [23, 22] one of the authors extended this method (for string rewriting) to arctic automata, i.e. on the max/plus semi-ring on {−∞}∪N.  ... 
doi:10.1007/978-3-540-70590-1_14 fatcat:tmc6gvkltjaobjnh2z2tzurmq4

Stream Differential Equations: Specification Formats and Solution Methods [article]

Helle Hvid Hansen, Clemens Kupke, Jan Rutten
2016 arXiv   pre-print
Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades.  ...  Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define.  ...  Term rewriting. Closely related to functional programming is the work on streams in term rewriting.  ... 
arXiv:1609.08367v1 fatcat:pwvidt3ubbfxdpsr2qqyyxs44m

Synchronization and Linearity: An Algebra for Discrete Event Systems

Charles Leake, Francois Baccelli, Guy Cohen, Geert Jan Olsder, Jean-Pierre Quadrat
1994 Journal of the Operational Research Society  
Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of  ...  About This and Future Releases We have taken the opportunity of this electronic edition to make corrections of misprints and slight mistakes we have become aware of since the book was published for the  ...  In §6.5 we discuss rationality in the max-plus context, and characterize rational elements in terms of periodicity. We also discuss the problem of minimal realization of these max-plus systems.  ... 
doi:10.2307/2583959 fatcat:cx7pfvwhk5cshanzmfjwzjyizy

Half a century after Carl Adam Petri's Ph.D. thesis: A perspective on the field

Manuel Silva
2013 Annual Reviews in Control  
for Standardization) or IEC (International Electrotechnical Commission) standards for the use of Petri nets in engineering, this work cannot hope to be a complete survey or a tutorial in the more classical  ...  It is more of an impressionistic overview of the field.  ...  We are also very grateful for their helpful advice to Sebastián Dormido (Madrid, SP), Janan Zaytoon (Reims, FR) and several (ex)members of our Grupo de Ingeniería de Sistemas de Eventos Discretos (GISED  ... 
doi:10.1016/j.arcontrol.2013.09.001 fatcat:othq33ivp5hdtpxqiwznkek6pe

OASIcs, Volume 13, MEMICS'09, Complete Volume [article]

Petr Hlinený, Václav Matyáš, Tomáš Vojnar
2012
Jørgensen and the anonymous reviewers for their comments and suggestions.  ...  Acknowledgements: The authors would like to thank Michael Weber for creating and helping us use the NIPS framework. Acknowledgements We would like to thank Jiří Srba, Mads Chr. Olesen, Kenneth Y.  ...  MPGs can even be used for solving the max-plus algebra Ax = Bx problem, which in turn has further applications [6] . MPGs are also important from a theoretical point of view.  ... 
doi:10.4230/oasics.memics.2009 fatcat:p4y674not5ecxbl7qujzp3eldy

Termination of rewriting and its certification [article]

Koprowski, A (Adam), Zantema, H (Hans), Groote, JF (Jan Friso)
2008
This is in fact a reachability problem for weighted (tree) automata.  ...  In [Wal07b, Wal07a] the matrix interpretations method was extended (for string rewriting) to the arctic domain, i.e., on the max/plus semiring on Ø¡ Ù N.  ...  Conclusions In this thesis we presented contributions to methods for producing proofs of termination of term rewriting systems and to certification of such proofs.  ... 
doi:10.6100/ir637480 fatcat:ggp5vkajkbajho2gyxvvwgukpq

Timing analysis of synchronous data flow graphs [article]

Ghamarian, AH (Amir), Otten, RHJM (Ralph), Basten, AA (Twan), Geilen, MCW (Marc)
2008
Max-Plus matrix equation.  ...  Max-Plus Algebraic Characterization A very elegant model to reason about (H)SDFGs is the Max-Plus algebra [3, 13] .  ... 
doi:10.6100/ir635718 fatcat:bcrbtjr4lfa37hekonk2bligp4
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