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Well-quasi-orders and regular ω-languages

Mizuhito Ogawa
2004 Theoretical Computer Science  
We extend this result to regular !-languages. That is, (1) an !-language L is regular if and only if L is 4-closed under a periodic extension 4 of some monotone WQO over ÿnite words, and (2) an !  ...  In "On regularity of context-free languages" [Theoret. Comput.  ...  This research is supported by Special Coordination Funds for Promoting Science and Technology by Ministry of Education, Culture, Sports, Science and Technology, and Kayamori Foundation of Informational  ... 
doi:10.1016/j.tcs.2004.03.052 fatcat:tvvxsyevhbhqnpy4nlu2rbnxvi

Well Quasi-Orders in Computer Science (Dagstuhl Seminar 16031)

Jean Goubault-Larrecq, Monika Seisenberger, Victor Selivanov, Andreas Weiermann, Marc Herbstritt
2016 Dagstuhl Reports  
of Well quasi-orders (known as the Wqo-Theory) and several fields of Computer Science (Verification and Termination of Infinite-State Systems, Automata and Formal Languages, Term Rewriting and Proof Theory  ...  , topological complexity of computational problems on continuous functions).  ...  The topic Automata and Formal Languages was surveyed by Mizuhito Ogawa on Thursday morning who summarized several interesting facts relating WQOs to popular classes of languages and ω-languages on words  ... 
doi:10.4230/dagrep.6.1.69 dblp:journals/dagstuhl-reports/Goubault-Larrecq16 fatcat:o3uwzu5ptfavfes6kgexpi4a6q

Well Quasiorders and Hierarchy Theory [article]

Victor Selivanov
2018 arXiv   pre-print
While the classical hierarchies of sets usually degenerate to structures very close to ordinals, the extension of them to functions requires more complicated WQOs, and the same applies to reducibilities  ...  We discuss some applications of WQOs to several fields were hierarchies and reducibilities are the principal classification tools, notably to Descriptive Set Theory, Computability theory and Automata Theory  ...  I am grateful to Leibniz-Zentrum für Informatik for accepting and taking care of Dagstuhl Seminars 08271, 11411, 15392, 16031 which were important for promoting the topic of this paper.  ... 
arXiv:1809.02941v1 fatcat:7ztqokcr7ret3fiusnzszegyxa

The Ideal Theory for WSTS [chapter]

Alain Finkel
2016 Lecture Notes in Computer Science  
We argue that the theory of ideals prompts a renewal of the theory of WSTS by providing a way to define a new class of monotonic systems, the so-called Well Behaved Transition Systems, which properly contains  ...  We then recall the completion of WSTS which leads to defining a conceptual Karp-Miller procedure that terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets.  ...  Acknowledgement I would like to thank Michael Blondin, Jean Goubault-Larrecq and Pierre McKenzie for fruitful discussions and for having allowed me to use some parts of common papers.  ... 
doi:10.1007/978-3-319-45994-3_1 fatcat:ym2cdxqginagtk2kvoiuip6l5m

A new order theory of set systems and better quasi-orderings [article]

Yohji Akama
2012 arXiv   pre-print
We prove that the class of set systems corresponding to BQOs is closed by any monotone function. In (Shinohara and Arimura.  ...  The theory of this new order type and continuous, monotone function between set systems corresponds to the theory of well quasi-orderings (WQOs).  ...  Special thanks go to Ken-ichi Kawarabayashi for his encouragement after the 11-March earthquake.  ... 
arXiv:1112.2801v3 fatcat:yipvi2he3vfxnaurgbrpcnouu4

A new order theory of set systems and better quasi-orderings

Yohji AKAMA
2012 Progress in Informatics  
We prove that the class of set systems corresponding to BQOs is closed by any monotone function. In (Shinohara and Arimura.  ...  The theory of this new order type and continuous, monotone function between set systems corresponds to the theory of well quasi-orderings (WQOs).  ...  Special thanks go to Ken-ichi Kawarabayashi for his encouragement after the 11-March earthquake.  ... 
doi:10.2201/niipi.2012.9.3 fatcat:xcqk5yadqzgp7bceqc5oobsb74

Complete Abstractions for Checking Language Inclusion

Pierre Ganty, Francesco Ranzato, Pedro Valero
2021 ACM Transactions on Computational Logic  
This overapproximating abstraction of languages can be defined using quasiorder relations on words, where the abstraction gives the language of all the words "greater than or equal to" a given input word  ...  trace sets of one-counter nets, and context-free languages into regular languages.  ...  This general framework is instantiated in Section 5 to the class of abstractions induced by wellquasiorders on words, thus yielding effective inclusion checking algorithms for regular languages and traces  ... 
doi:10.1145/3462673 fatcat:tcsctqd5sfbina22iadukl5tru

Well quasi-orders, unavoidable sets, and derivation systems

Flavio D'Alessandro, Stefano Varricchio
2006 RAIRO - Theoretical Informatics and Applications  
We prove that the set I is unavoidable if and only if the relation ⇒ * I is a well quasi-order on the set L I . This result generalizes a theorem of [Ehrenfeucht et al., Theor. Comput.  ...  Let I be a finite set of words and ⇒ * I be the derivation relation generated by the set of productions { → u | u ∈ I}. Let L I be the set of words u such that ⇒ * I u.  ...  We kindly acknowledge Gwénaël Richomme for several useful comments on the first version of this paper.  ... 
doi:10.1051/ita:2006019 fatcat:sgsbj3whybf37k3ncqqgttx2eq

Computable fixpoints in well-structured symbolic model checking

N. Bertrand, P. Schnoebelen
2012 Formal methods in system design  
systems where nesting and alternation of least and greatest fixpoints are common.  ...  This has immediate applications for the verification of wellstructured systems, where a main issue is the computability of fixpoint expressions, and in particular for game-theoretical properties and probabilistic  ...  Acknowledgements This article is a long and improved version of a conference paper originally coauthored with Christel Baier [14] .  ... 
doi:10.1007/s10703-012-0168-y fatcat:4tbjrq4btnhfjnty6agtszkosu

PTL-separability and closures for WQOs on words [article]

Georg Zetzsche
2018 arXiv   pre-print
Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of upward closed sets. In this way, a range of regular language classes arises as PTLs.  ...  First, we study which (perhaps non-regular) language classes permit a decision procedure to decide whether two given languages are separable by a PTL with respect to a given WQO.  ...  The author is very grateful to Wojciech Czerwiński, Sylvain Schmitz, and Marc Zeitoun for discussions that yielded important insights.  ... 
arXiv:1802.07397v1 fatcat:rbfrgx4jcfh23g272lr5mljcay

Well-structured languages

Gilles Geeraerts, Jean-François Raskin, Laurent Van Begin
2007 Acta Informatica  
Acknowledgements The authors would like to express their gratitude to the anonymous referee, whose comments have definitely contributed to improve the present paper.  ...  WSTS [10] are transition systems whose state space is infinite but equipped with a well-quasi ordering (wqo for short) and whose transition relation is monotonic w.r.t. this wqo.  ...  In accordance to previous classical works on the expressive power of Petri nets, we distinguish several classes of languages of WSTS, depending on the form of the set of accepting states.  ... 
doi:10.1007/s00236-007-0050-3 fatcat:o2ynn2rqqbgrffybm3u44o3gna

Complete Abstractions for Checking Language Inclusion [article]

Pierre Ganty, Francesco Ranzato, Pedro Valero
2021 arXiv   pre-print
This overapproximating abstraction of languages can be defined using quasiorder relations on words, where the abstraction gives the language of all the words "greater than or equal to" a given input word  ...  trace sets of one-counter nets, and context-free languages into regular languages.  ...  Backward completeness for right concatenation is proven similarly by relying on the right monotonicity of . Proof of Theorem 7.5: Let L2 a decidable L 2 -consistent wqo on Σ * .  ... 
arXiv:1904.01388v2 fatcat:bonus6qhpzcnfbveqd6pdkbgd4

Forward Analysis for WSTS, Part II: Complete WSTS [chapter]

Alain Finkel, Jean Goubault-Larrecq
2009 Lecture Notes in Computer Science  
We show that such completions are ∞-complete exactly when X is an ω 2 -WSTS , a new robust class of WSTS.  ...  We show that our procedure terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets and on lossy channel systems.  ...  Acknowledgement The authors wish to acknowledge fruitful discussions with Sylvain Schmitz, and to thank the anonymous referees for their comments.  ... 
doi:10.1007/978-3-642-02930-1_16 fatcat:a76wgecdrnbopp57rn7nmamb64

Forward Analysis for WSTS, Part II: Complete WSTS

Alain Finkel, Jean Goubault-Larrecq, Wolfgang Thomas
2012 Logical Methods in Computer Science  
We show that such completions are infinity-complete exactly when X is an omega-2-WSTS, a new robust class of WSTS.  ...  We show that our procedure terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets and on lossy channel systems.  ...  Acknowledgement The authors wish to acknowledge fruitful discussions with Sylvain Schmitz, and to thank the anonymous referees for their comments.  ... 
doi:10.2168/lmcs-8(3:28)2012 fatcat:qpeiydtjbfamhnojvndeavwijm

Certified Kruskal's Tree Theorem [chapter]

Christian Sternagel
2013 Lecture Notes in Computer Science  
For example, the theory of simplification orders [Der82, MZ97] was formalized -on top of the presented workas part of IsaFoR, 2 where it is applied to show well-foundedness of the Knuth-Bendix order [ST13  ...  sequences of elements to be "good").  ...  Parts of the presented formalization were used by Wu et al. [WZU11] to formalize a proof of: For every language A, the languages of sub-and superstrings of A are regular.  ... 
doi:10.1007/978-3-319-03545-1_12 fatcat:ojh6mrcaxzfgdjtr6gfjlbkmgy
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