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An undecidable property of context-free languages [article]

Zoltan Esik
2010 arXiv   pre-print
As a corollary to this result, we show that it is undecidable whether the lexicographic orderings of the languages generated by two context-free grammars have the same order type.  ...  We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering.  ...  Here, we show that it is undecidable for context-free linear orderings (given by context-free grammars) whether they are isomorphic.  ... 
arXiv:1004.1736v1 fatcat:xthg5v4o3rcorbrvmjyp7dimpe

A note on undecidable properties of formal languages

Sheila Greibach
1968 Mathematical Systems Theory  
For example, to establish that it is undecidable whether a context-free language is, say, metalinear, we need only find a context-free language that is not metalinear.  ...  Many of the properties enjoyed by such families as the context-free languages, one-way stack languages, and some complexity classes of languages defined by Turing machines can be established uniformly  ...  It is undecidable whether the complement of a context-free language is (a) regular, (b) linear context-free, (c) context-free. COROLLARY.  ... 
doi:10.1007/bf01691341 fatcat:dehwnwom55curcxwfvsosq6yxe

A Context-Free Linear Ordering with an Undecidable First-Order Theory [chapter]

Arnaud Carayol, Zoltán Ésik
2012 Lecture Notes in Computer Science  
In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.  ...  The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering.  ...  The authors would like to thank Markus Lohrey for his remarks on a previous draft of this article as well as for the proof of Proposition 3.  ... 
doi:10.1007/978-3-642-33475-7_8 fatcat:gbahtnohbnhtjapyxi6eobm53m

Page 4630 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
The paper determines the space and time complexity of the fixed and general membership problems for external and inter- nal contextual languages with finite, regular, linear context-free, context-free  ...  We investigate decidability problems and prove that some properties that are undecidable for general context-free languages become decidable for XML-languages.  ... 

A note on the undecidability of contextfreeness

J. Albert
1982 RAIRO Informatique théorique  
ALBERT The problem, whether a language contains an infinité regular set-is an 1RS language -is decidable for the deterministic context-free languages and undecidable for the linear context-free languages  ...  , = £*" is undecidable for linear context-free languages L. In [12] a rather genera!  ... 
doi:10.1051/ita/1982160100031 fatcat:j3elepwsqjfenn5mlohx4froni

Undecidable properties of monoids with word problem solvable in linear time. Part II— cross sections and homological and homotopical finiteness conditions

Masashi Katsura, Yuji Kobayashi, Friedrich Otto
2003 Theoretical Computer Science  
These properties include the existence of context-free or regular cross-sections, the existence of ÿnite convergent presentations, the property of being automatic, and the homological and homotopical ÿniteness  ...  Expanding on this construction it is shown here that also many properties that are not known to be linear Markov properties are undecidable for this class of monoids.  ...  Acknowledgements We are grateful to the referees whose questions and detailed comments helped to greatly improve the presentation of this paper.  ... 
doi:10.1016/s0304-3975(02)00570-4 fatcat:or3c3kasgzerlpr5lqgukxdgnm

Page 5456 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Summary: “For a class & of languages, an /-controlled linear grammar K consists of a linear context-free grammar G and a control language H in , where the terminals of H are interpreted as the labels of  ...  For this purpose, a language for the specification of context-free tree grammars is defined. This language is extended to an attribute tree grammar specification language.”  ... 

Page 1575 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Summary: “Context unification is a particular case of second- order unification in which all second-order variables are unary and only linear functions are sought as solutions.  ...  of one and two successors and the decid- ability of the monadic second-order theory of linear order (Biichi, Rabin).  ... 

The inclusion problem for some subclasses of context-free languages

Peter R.J. Asveld, Anton Nijholt
2000 Theoretical Computer Science  
By a reduction to Post's Correspondence Problem we provide a direct proof of the known fact that the inclusion problem for unambiguous context-free grammars is undecidable.  ...  The argument or some straightforward modiÿcation also applies to some other subclasses of context-free languages such as linear languages, sequential languages, and DSC-languages (i.e., languages generated  ...  Acknowledgements We are indebted to Rieks op den Akker and Jan Anne Hogendorp for some remarks on an earlier version of this note.  ... 
doi:10.1016/s0304-3975(99)00113-9 fatcat:6236w3qpxfgynffdd34bpuwsxm

Page 5102 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
It is shown that ALD languages enjoy the noncounting property of paren- thesized context-free languages (stencil tree languages).  ...  Summary: “It is undecidable whether or not a given context-free language and a propagating DTOL language are equal.  ... 

Pseudo-inversion on Formal Languages [chapter]

Da-Jung Cho, Yo-Sub Han, Shin-Dong Kang, Hwee Kim, Sang-Ki Ko, Kai Salomaa
2014 Lecture Notes in Computer Science  
We establish that pseudo-inversion-freeness is decidable in polynomial time for regular languages and undecidable for context-free languages.  ...  Finally, we introduce the pseudo-inversion-freeness and examine closure properties and decidability problems for regular and context-free languages.  ...  We have designed a polynomialtime algorithm for regular languages and established an undecidability result for linear context-free languages.  ... 
doi:10.1007/978-3-319-08123-6_8 fatcat:pwyz2q3rnndnfn2gicwz3cmrmu

Page 4946 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
problem but undecidable linear equational matching.”  ...  of context-free languages.  ... 

A Modal Fixpoint Logic with Chop [chapter]

Markus Müller-Olm
1999 Lecture Notes in Computer Science  
We show that any context-free process can be characterized by an FLC-formula up to bisimulation or simulation.  ...  and validity are undecidable; FLC does not have the finite-model property.  ...  FLC is undecidable for context-free processes.  ... 
doi:10.1007/3-540-49116-3_48 fatcat:xpvoo6g7ynhdxg3ylrzixwmyo4

Page 4266 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
Among the applications of this theorem, the undecidability for regularity of the language generated by a context-free grammar and for the problem of inherent ambiguity of c.f.l. is given.  ...  A special section is devoted to the Greibach theorem for proving undecidability of properties.  ... 

Page 516 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
the first-order theory of set constraints with the union operator is undecidable.  ...  3*V*-fragment of the first-order theory of one- step-rewriting by R is undecidable; the emptiness problem for tree automata with equality tests between cousins is undecidable; and the 3*V*-fragment of  ... 
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