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Deciding Piecewise Testable Separability for Regular Tree Languages

Jean Goubault-Larrecq, Sylvain Schmitz, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
In the case of finite ranked trees ordered by homeomorphic embedding, we show using effective representations for tree ideals that it entails the decidability of piecewise testable separability when the  ...  A final byproduct is a new proof of the decidability of whether an input regular language of ranked trees is piecewise testable, which was first shown in the unranked case by Bojańczyk, Segoufin, and Straubing  ...  For instance, can one derive the characteristic equations of Bojańczyk et al. [6] for piecewise-testable tree languages from Lemma 12? Acknowledgements.  ... 
doi:10.4230/lipics.icalp.2016.97 dblp:conf/icalp/Goubault-Larrecq16 fatcat:6kzs33bamfgvlhuor72x7o4nra

Separability by Piecewise Testable Languages is PTime-Complete [article]

Tomáš Masopust
2017 arXiv   pre-print
Two regular languages are separable by a piecewise testable language if the piecewise testable language includes one of them and is disjoint from the other.  ...  The main result is then the lower-bound complexity of separability of regular languages by piecewise testable languages.  ...  Acknowledgements The author is very grateful toŠtěpán Holub for his comments on the preliminary version of this work, and to an anonymous reviewer for valuable comments.  ... 
arXiv:1704.07856v2 fatcat:2w6d7obnpbdnhnyywy5z6tjaca

The separation problem for regular languages by piecewise testable languages [article]

Lorijn van Rooijen, Marc Zeitoun
2013 arXiv   pre-print
We present and discuss the separation problem for regular languages.  ...  We then give a direct polynomial time algorithm to check whether two given regular languages are separable by a piecewise testable language, that is, whether a BΣ1(<) sentence can witness that the languages  ...  One can decide in PTIME whether two languages can be separated by a prefix-testable language. A simple PTIME algorithm for separation by a piecewise testable language Piecewise testable languages.  ... 
arXiv:1303.2143v1 fatcat:7dcxkehrezgyxfvbjc3q7pmkdy

Piecewise testable tree languages

Mikołaj Bojańczyk, Luc Segoufin, Howard Straubing, Wolfgang Thomas
2012 Logical Methods in Computer Science  
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences.  ...  This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma_1 sentences if and only if its syntactic monoid is J-trivial.  ...  It is decidable if a regular forest language is commutative-cca-piecewise testable. 6.3. Tree languages.  ... 
doi:10.2168/lmcs-8(3:26)2012 fatcat:3qlytoya4jg4rfolvbhitoh7u4

Piecewise Testable Tree Languages

Mikolaj Bojanczyk, Luc Segoufin, Howard Straubing
2008 Logic in Computer Science  
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Σ 1 sentences.  ...  This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Σ 1 sentences if and only if its syntactic monoid is J -trivial.  ...  It is decidable if a regular forest language is commutative-cca-piecewise testable. 6.3. Tree languages.  ... 
doi:10.1109/lics.2008.46 dblp:conf/lics/BojanczykSS08 fatcat:e4bfnwfozre6zhwdgmuiqesq74

A Characterization for Decidable Separability by Piecewise Testable Languages [article]

Wojciech Czerwiński, Wim Martens, Lorijn van Rooijen, Marc Zeitoun, Georg Zetzsche
2017 arXiv   pre-print
In this work, we assume some mild closure properties for C and study for which such classes separability by a piecewise testable language (PTL) is decidable.  ...  In fact, for all (non-regular) language classes that we present as examples with decidable separability, it is undecidable whether a given language is a PTL itself.  ...  Acknowledgments We would like to thank Tomáš Masopust for pointing us to (Hunt III, 1982) and Thomas Place for pointing out to us that determining if a given context-free language is piecewise testable  ... 
arXiv:1410.1042v3 fatcat:hzgrzuioq5fjjkqxvpsoet4al4

Partially Ordered Automata and Piecewise Testability [article]

Tomáš Masopust, Markus Krötzsch
2021 arXiv   pre-print
For instance, the fragment of first-order formulae with a single existential block of quantifiers in prenex normal form is known as piecewise testable languages or J-trivial languages.  ...  We show that deciding universality for general ptNFAs is as hard as for general NFAs.  ...  Polák for providing us with their manuscript [34] , and we gratefully acknowledge very useful suggestions and comments of the anonymous referees.  ... 
arXiv:1907.13115v7 fatcat:lfiveyx5gjcktor467o5mkcfwe

Efficient Separability of Regular Languages by Subsequences and Suffixes [article]

Wojciech Czerwiński and Wim Martens and Tomáš Masopust
2013 arXiv   pre-print
When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof.  ...  We give characterizations of when two languages can be separated and present an overview of when these problems can be decided in polynomial time if K and L are given by nondeterministic automata.  ...  We are grateful to Miko laj Bojańczyk, who pointed out the connection between layered separability and boolean combinations.  ... 
arXiv:1303.0966v1 fatcat:igjhk3e3ajh5rerzaemwmhxq5i

Alternating Towers and Piecewise Testable Separators [article]

Štěpán Holub and Tomáš Masopust and Michaël Thomazo
2015 arXiv   pre-print
Two languages are separable by a piecewise testable language if and only if there exists no infinite tower between them.  ...  For regular languages represented by nondeterministic finite automata, the existence of an infinite tower is decidable in polynomial time.  ...  Acknowledgements The authors would like to thank Stefan Borgwardt, Wojciech Czerwiński, Galina Jirásková, Markus Krötzsch, and Wim Martens for valuable discussions on various parts of the paper.  ... 
arXiv:1409.3943v2 fatcat:qm7gkbvw5rahtod7uvkzro6sva

Efficient Separability of Regular Languages by Subsequences and Suffixes [chapter]

Wojciech Czerwiński, Wim Martens, Tomáš Masopust
2013 Lecture Notes in Computer Science  
When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewiseand suffix-testable languages and variants thereof.  ...  We give characterizations of when two languages can be separated and present an overview of when these problems can be decided in polynomial time if K and L are given by nondeterministic automata.  ...  We are grateful to Miko laj Bojańczyk, who pointed out the connection between layered separability and boolean combinations.  ... 
doi:10.1007/978-3-642-39212-2_16 fatcat:ph2ifjvld5chlkabg6tbv33oky

On k-piecewise testability (preliminary report) [article]

Tomáš Masopust, Michaël Thomazo
2015 arXiv   pre-print
We study the following problem: Given a DFA recognizing a piecewise testable language, decide whether the language is k-PT. We provide a complexity bound and a detailed analysis for small k's.  ...  For a non-negative integer k, a language is k-piecewise testable (k-PT) if it is a finite boolean combination of languages of the form Σ^* a_1 Σ^* ...Σ^* a_n Σ^* for a_i∈Σ and 0< n < k.  ...  We thank an anonymous reviewer for informing us about the unpublished manuscript [24] and its authors for providing it. It shows that the k-PT problem is co-NP-complete for k ≥ 4.  ... 
arXiv:1412.1641v2 fatcat:orcnn2qxojewlmddclfsc5frxa

Typology emerges from simplicity in representations and learning

Dakotah Jay Lambert, Jonathan Rawski, Jeffrey Heinz
2021 Journal of Language Modelling  
The same learning algorithms, however, can be applied to model-theoretic treatments of other linguistic representations such as syntactic trees or autosegmental graphs, which opens a useful direction for  ...  We derive well-understood and well-studied subregular classes of formal languages purely from the computational perspective of algorithmic learning problems.  ...  , Caron (1998, see also Caron 2000) describe algorithms that decide whether the corresponding language is Locally or Piecewise Testable.  ... 
doi:10.15398/jlm.v9i1.262 fatcat:idvswelekngjxk3jbuecyq7zz4

Regular Separability of Parikh Automata [article]

Lorenzo Clemente, Wojciech Czerwiński, Sławomir Lasota, Charles Paperman
2016 arXiv   pre-print
is undecidable for this model, we show surprising decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is disjoint from  ...  While the regularity problem (is the language of a given automaton regular?)  ...  Separability problems for regular languages attracted recently a lot of attention, which resulted in establishing the decidability of F separability for the family F of separators being the piecewise testable  ... 
arXiv:1612.06233v1 fatcat:z3va4zfkxjc3pn6rklhbegh474

Deciding Universality of ptNFAs is PSpace-Complete [chapter]

Tomáš Masopust, Markus Krötzsch
2017 Lecture Notes in Computer Science  
We study the universality problem for ptNFAs, a class of partially ordered NFAs recognizing piecewise testable languages.  ...  Deciding universality for both NFAs and partially ordered NFAs is PSpace-complete. For ptNFAs, the complexity drops to coNP-complete if the alphabet is fixed but is open if the alphabet may grow.  ...  Simon [31] showed that piecewise testable languages are exactly those regular languages whose syntactic monoid is J -trivial and that they are characterized by confluent, partially ordered DFAs.  ... 
doi:10.1007/978-3-319-73117-9_29 fatcat:c2qvh4vfwzfbpj25yi25jkmbqy

Varieties [article]

Howard Straubing, Pascal Weil
2018 arXiv   pre-print
This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages.  ...  Our presentation of the theory draws heavily on the work of Gehrke, Grigorieff and Pin (2008) on the equational theory of lattices of regular languages.  ...  Decidability and equational description It is not clear that we can effectively decide whether a given regular language is piecewise testable.  ... 
arXiv:1502.03951v3 fatcat:6wcn4suoyjc2je7ip3ikcyoqaa
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