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An undecidable property of context-free languages
[article]

2010
*
arXiv
*
pre-print

As a corollary to this result, we show that it is

arXiv:1004.1736v1
fatcat:xthg5v4o3rcorbrvmjyp7dimpe
*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. ...##
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A note on undecidable properties of formal languages

1968
*
Mathematical Systems Theory
*

For example, to establish that it is

doi:10.1007/bf01691341
fatcat:dehwnwom55curcxwfvsosq6yxe
*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. ...##
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A Context-Free Linear Ordering with an Undecidable First-Order Theory
[chapter]

2012
*
Lecture Notes in Computer Science
*

In stark contrast, we give

doi:10.1007/978-3-642-33475-7_8
fatcat:gbahtnohbnhtjapyxi6eobm53m
*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. ...##
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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. ...##
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A note on the undecidability of contextfreeness

1982
*
RAIRO Informatique théorique
*

ALBERT The problem, whether a language contains

doi:10.1051/ita/1982160100031
fatcat:j3elepwsqjfenn5mlohx4froni
*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! ...##
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Undecidable properties of monoids with word problem solvable in linear time. Part II— cross sections and homological and homotopical finiteness conditions

2003
*
Theoretical Computer Science
*

These

doi:10.1016/s0304-3975(02)00570-4
fatcat:or3c3kasgzerlpr5lqgukxdgnm
*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. ...##
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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.” ...##
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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). ...##
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The inclusion problem for some subclasses of context-free languages

2000
*
Theoretical Computer Science
*

By a reduction to Post's Correspondence Problem we provide a direct proof

doi:10.1016/s0304-3975(99)00113-9
fatcat:6236w3qpxfgynffdd34bpuwsxm
*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. ...##
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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]

2014
*
Lecture Notes in Computer Science
*

We establish that pseudo-inversion-freeness is decidable in polynomial time for regular languages and

doi:10.1007/978-3-319-08123-6_8
fatcat:pwyz2q3rnndnfn2gicwz3cmrmu
*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. ...##
###
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]

1999
*
Lecture Notes in Computer Science
*

We show that any

doi:10.1007/3-540-49116-3_48
fatcat:xpvoo6g7ynhdxg3ylrzixwmyo4
*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. ...##
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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*. ...##
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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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