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On omega context free languages which are Borel sets of infinite rank

2003
*
Theoretical Computer Science
*

We proved in (Topological properties of

doi:10.1016/s0304-3975(02)00327-4
fatcat:uufsvfxyyzeufivmyrekrt3f3m
*omega*context free languages, Theoretical*Computer*Science, 262 (1-2) (2001) 669-697) that the class of ! ... -CFL exhausts the ÿnite ranks of the Borel hierarchy, and in (Borel hierarchy and*omega*context free languages, Theoretical*Computer*Science, to appear) that there exist some ! ... Acknowledgements Thanks to the anonymous referees for useful comments*on*a previous version of this paper. ...##
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Topological properties of omega context-free languages

2001
*
Theoretical Computer Science
*

This paper is a study of topological properties of

doi:10.1016/s0304-3975(00)00405-9
fatcat:3dxegiguxvcadifqzisxns5pay
*omega*context-free languages (!-CFL). We ÿrst extend some decidability results for the*deterministic**ones*(! ... Thesis, Università e Paris 7, March 1992) about*omega*powers of ÿnitary languages. We show that B uchi-Landweber's Theorem cannot be extended to even closed ! ... Thanks also to the anonymous referees for useful comments*on*a previous version of this paper. ...##
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On Omega Context Free Languages which are Borel Sets of Infinite Rank
[article]

2010
*
arXiv
*
pre-print

of Infinite

arXiv:1005.5633v1
fatcat:2vfujzo3bjb2bkfb7ajtngssry
*Computations*, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621]. ... This paper is a continuation of the study of topological properties of*omega*context free languages (*omega*-CFL). ... Thanks to the anonymous referees for useful comments*on*a previous version of this paper. ...##
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Borel Hierarchy and Omega Context Free Languages
[article]

2011
*
arXiv
*
pre-print

And

arXiv:1101.3443v1
fatcat:mchn5kjacvautj2yks4psn5aqa
*one*cannot decide whether an*omega*-CFL is a Borel set. ... Then we prove some recursive analogues to preceding properties: in particular*one*cannot decide whether an*omega*-CFL is an arithmetical set. ... Then at any moment of any*computation*the word in the*pushdown*store is in the form E n Z 0 where n is an integer ≥ 0. ...##
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Borel hierarchy and omega context free languages

2003
*
Theoretical Computer Science
*

-languages accepted by

doi:10.1016/s0304-3975(02)00042-7
fatcat:ea2ptno4wfhxrm25rvdcnf7z7y
*omega**pushdown*automata, considering various acceptance conditions for*omega*words. ... -regular language accepted by a B uchi automaton M , the resulting*machine*M is just a*one*counter*machine*, i.e. a*pushdown**machine*having a stack alphabet = {Z 0 ; E}, where Z 0 is the bottom symbol which ...##
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Wadge hierarchy of omega context-free languages

2001
*
Theoretical Computer Science
*

The main result of this paper is that the length of the Wadge hierarchy of

doi:10.1016/s0304-3975(01)00008-1
fatcat:gijdxowzszfcbekqgf7hxykxda
*omega*context-free languages is greater than the Cantor ordinal 0, and the same result holds for the conciliating Wadge hierarchy ... In the course of our proof, we get results*on*the Wadge hierarchy of iterated counter !-languages, which we deÿne as an extension of classical (ÿnitary) iterated counter languages to !-languages. ... As in the general case of*pushdown**machines*, we can consider together ÿnite and inÿnite runs of a k-iterated counter*pushdown**machine*given with two state sets K 1 and K 2 (*one*is used for the acceptation ...##
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Omega Automata and its Classes

2018
*
Current Science
*

In addition, this paper also summarizes the applicability of

doi:10.18520/cs/v115/i11/2042-2051
fatcat:byu5hbxpnbaclbp2rkx3qa6uhm
*omega*automata in various interdisciplinary fields. ... Language generated by*omega*-automata is used for representing non-terminating*computations*. ... (iv) Equivalence problem for ω*deterministic**pushdown*automata is still an open problem. (v) The concept of visibly*pushdown*automata and infinity games can be explored in the near future. ...##
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Good-for-games $\omega$-Pushdown Automata

2022
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Logical Methods in Computer Science
*

We introduce good-for-games $\

doi:10.46298/lmcs-18(1:3)2022
fatcat:2nm6ks4rz5efznj3bgpw6md2ay
*omega*$-*pushdown*automata ($\*omega*$-GFG-PDA). These are automata whose nondeterminism can be resolved based*on*the input processed so far. ... Our main results are that $\*omega*$-GFG-PDA are more expressive than*deterministic*$\*omega*$-*pushdown*automata and that solving infinite games with winning conditions specified by $\*omega*$-GFG-PDA is EXPTIME-complete ... This is beyond the capabilities of finite-state*machines*and blocks the stack of a*pushdown**machine*implementing r from performing other*computations*. ...##
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Decision Problems for Deterministic Pushdown Automata on Infinite Words

2014
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Electronic Proceedings in Theoretical Computer Science
*

The article surveys some decidability results for DPDAs

doi:10.4204/eptcs.151.4
fatcat:gxxf7gxwmnhnfmgvsjiskdoj3y
*on*infinite words (*omega*-DPDA). ... Furthermore, we present some new results*on*the parity index problem for*omega*-DPDAs. ... We are mainly concerned with*deterministic**pushdown*automata in this work. We first define*pushdown**machines*, which are*pushdown*automata without acceptance condition. ...##
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Ambiguity in omega context free languages

2003
*
Theoretical Computer Science
*

-CFL) accepted by B uchi or Muller

doi:10.1016/s0304-3975(02)00584-4
fatcat:zohu57u5t5dzrh6yjhpiqdf2pe
*pushdown*automata. We show that these notions may be deÿned independently of the B uchi or Muller acceptance condition which is considered. ... We extend the well-known notions of ambiguity and of degrees of ambiguity of ÿnitary context free languages to the case of*omega*context free languages (! ... Acknowledgements Thanks to Jean-Pierre Ressayre and Jacques Duparc for many useful discussions about Wadge and Wagner hierarchies, and to Pierre Simonnet for communicating his result*on*analytic*omega*...##
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Page 2219 of Mathematical Reviews Vol. , Issue 91D
[page]

1991
*
Mathematical Reviews
*

(F-PARIS7-LI)

*Pushdown*automata*on*infinite trees and*omega*-Kleene closure of context-free tree sets. ... / log n) time bound for the simulation of a*deterministic*f(n) time-bounded multi- tape Turing*machine**on*a*deterministic**one*-tape off-line Turing*machine*and to an O(n*/,/logn) time bound for transposing ...##
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Topological Complexity of Context-Free omega-Languages: A Survey
[article]

2013
*
arXiv
*
pre-print

In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-

arXiv:0806.1413v2
fatcat:jx2eoqnupbdg3eyynkz3u2ygbi
*deterministic*or*deterministic*context-free*omega*-languages. ... We survey recent results*on*the topological complexity of context-free*omega*-languages which form the second level of the Chomsky hierarchy of languages of infinite words. ... Unlike the case of finite automata,*deterministic*M P DA do not define the same class of ω-languages as non*deterministic*M P DA. Let us now define*deterministic**pushdown**machines*. Definition 9. ...##
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Highly Undecidable Problems For Infinite Computations
[article]

2009
*
arXiv
*
pre-print

These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite

arXiv:0901.0373v1
fatcat:hto3r4zibjbz7byafrgurbdw5q
*machines*like 1-counter automata or 2-tape automata. ... Topological and arithmetical properties of 1-counter*omega*-languages, context free*omega*-languages, or infinitary rational relations, are also highly undecidable. ...*On*the other hand, an ω-language L ⊆ X ω is in the class Σ 1 1 iff it is accepted by a non*deterministic*Turing*machine*with a 1 ′ or Büchi acceptance condition, [Sta97] . ...##
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Topology and Ambiguity in Omega Context Free Languages
[article]

2008
*
arXiv
*
pre-print

In particular, using known facts from classical descriptive set theory, we prove that non Borel

arXiv:0801.0533v1
fatcat:upiqvt2lavebtfbhsu24vrxney
*omega*context free languages which are recognized by B\"uchi*pushdown*automata have a maximum degree of ambiguity ...*On*the other side we show that methods used in the study of*omega*context free languages can also be applied to study the notion of ambiguity in infinitary rational relations accepted by B\"uchi 2-tape ... We thank Dominique Lecomte and Jean-Pierre Ressayre for useful discussions and the anonymous referees for useful comments*on*a preliminary version of this paper. ...##
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Property grammars and table machines

1968
*
9th Annual Symposium on Switching and Automata Theory (swat 1968)
*

., A Regularity Test for

doi:10.1109/swat.1968.23
dblp:conf/focs/StearnsL68
fatcat:a6z3qaeg7ffw5nlqxxtjzefl44
*Pushdown**Machines*, Information & Control, vol. 11, #1, Sept. 1967, 323-340. 17. ... time*on*Turing*machines*and developed a theory of complexity classes. ...
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