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Topology and Ambiguity in Omega Context Free Languages [article]

Olivier Finkel
2008 arXiv   pre-print
We study the links between the topological complexity of an omega context free language and its degree of ambiguity.  ...  In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free languages which are recognized by B\"uchi pushdown automata have a maximum degree of ambiguity  ...  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.  ... 
arXiv:0801.0533v1 fatcat:upiqvt2lavebtfbhsu24vrxney

Omega Automata and its Classes

Natasha Singh, Ajay Kumar
2018 Current Science  
In addition, this paper also summarizes the applicability of omega automata in various interdisciplinary fields.  ...  This paper summarizes various types of ω-automata, their transition functions and accepting conditions.  ...  Language generated by omega-automata is used for representing non-terminating computations.  ... 
doi:10.18520/cs/v115/i11/2042-2051 fatcat:byu5hbxpnbaclbp2rkx3qa6uhm

Ambiguity in omega context free languages

Olivier Finkel
2003 Theoretical Computer Science  
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 (!  ...  We investigate ÿrst properties of the subclasses of omega context free languages we get in that way, giving many examples and studying topological properties of !-CFL of a given degree of ambiguity.  ...  context free languages.  ... 
doi:10.1016/s0304-3975(02)00584-4 fatcat:zohu57u5t5dzrh6yjhpiqdf2pe

Highly Undecidable Problems For Infinite Computations [article]

Olivier Finkel
2009 arXiv   pre-print
Topological and arithmetical properties of 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are also highly undecidable.  ...  for context-free omega-languages or for infinitary rational relations.  ...  Thus in that case R(T H ′ •H•θ(z) ) is a synchronized rational relation accepted by a deterministic, hence also non ambiguous, 2-tape Büchi automaton.  ... 
arXiv:0901.0373v1 fatcat:hto3r4zibjbz7byafrgurbdw5q

On Winning Conditions of High Borel Complexity in Pushdown Games [article]

Olivier Finkel
2008 arXiv   pre-print
are non-deterministic non-ambiguous context free languages, inherently ambiguous context free languages, or even non context free languages.  ...  We first show that, for every positive integer n, the class C_n(A), which arises in the definition of decidable winning conditions, is included in the class of non-ambiguous context free omega languages  ...  We give a positive answer to this question, giving examples of winning sets which are non-deterministic non-ambiguous context free languages, or inherently ambiguous context free languages, or even non  ... 
arXiv:0803.1830v1 fatcat:agj5cnfuk5f2rdxzgjepfcfgoq

Ambiguity, Weakness, and Regularity in Probabilistic Büchi Automata [article]

Christof Löding, Anton Pirogov
2020 arXiv   pre-print
In this work we extend the known classes of restricted PBA which are still regular, strongly relying on notions concerning ambiguity in classical omega-automata.  ...  PBA are known to accept, in general, a class of languages that goes beyond the regular languages.  ...  . countably ambiguous) that accept non-regular languages under almost-sure semantics.  ... 
arXiv:2004.13692v1 fatcat:psbgwb4nqzcd7kp24qldndp3tm

On the computation of covert channel capacity

Eugene Asarin, Cătălin Dima
2010 RAIRO - Theoretical Informatics and Applications  
We give three possible statements of the notion of "covert channel capacity" and relate the different definitions.  ...  We then provide several methods allowing the computation of lower and upper bounds for the capacity of a channel.  ...  Choffrut and S. Grigorieff from [4] .  ... 
doi:10.1051/ita/2010004 fatcat:buwjc3hnijgrxcd5vlpzqnx3fy

Semigroups and Automata on Infinite Words [chapter]

Dominique Perrin, Jean-Eric Pin
1995 Semigroups, Formal Languages and Groups  
Acknowledgements The authors would like to thank Olivier Carton and Pascal Weil for their comments on a preliminary version of this article.  ...  The con-nection between deterministic and non deterministic Büchi automata was enlightened by a deep theorem of McNaughton: a set of infinite words is recognized by a non deterministic Büchi automaton  ...  This is true for instance for the equivalence between deterministic and non deterministic automata and for the variety theorem.  ... 
doi:10.1007/978-94-011-0149-3_3 fatcat:baawnkgzrbdenmohs5wv3mgr6y

Probabilistic Grammars for Equation Discovery [article]

Jure Brence and Ljupčo Todorovski and Sašo Džeroski
2021 arXiv   pre-print
Deterministic grammars, such as context-free grammars, have been used to limit the search spaces in equation discovery by providing hard constraints that specify which equations to consider and which not  ...  We demonstrate that the use of probabilistic, rather than deterministic grammars, in the context of a Monte-Carlo algorithm for grammar-based equation discovery, leads to more efficient equation discovery  ...  P5-0093 and projects No. N2-0128, No. V5-1930. We would also like to thank Jovan Tanevski for providing feedback on early drafts of the manuscript.  ... 
arXiv:2012.00428v2 fatcat:dswqjncbpjch3fd6r2cvbajtsa

Reference list of indexed articles

1999 Theoretical Computer Science  
Takahashi, The greatest fixed-points and rational omega-tree languages 44 (3) (1986) 259-274 872. H.-J. Kreowski and A.  ...  Arnold, Rational w-languages are non-ambiguous 26 (1-2) (1983) 221-223 527. V. Rajlich, Determinism in parallel systems 26 (1-2) (1983) 225-23 1 528. W. Bucher and J.  ... 
doi:10.1016/s0304-3975(98)00320-x fatcat:bdgg2ekzdjahdo7g2gtwbdye6m

Do Gödel's Incompleteness Theorems Set Absolute Limits on the Ability of the Brain to Express and Communicate Mental Concepts Verifiably?

Bhupinder Singh Anand
2007 NeuroQuantology  
propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable.  ...  its mathematical propositions to be interpreted ambiguously.  ...  If we accept the classical definition of a number as real if, and only if, it is the limit of a Cauchy sequence 50 of rational numbers 51 , and that of a sequence of rationals as a function whose domain  ... 
doi:10.14704/nq.2004.2.2.39 fatcat:z6r3fnl45ba3fpxk4oj5xl26rm

Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably? [article]

Bhupinder Singh Anand
2004 arXiv   pre-print
However, a language of general, scientific, discourse cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth verifiably.  ...  We show how some paradoxical concepts of Quantum mechanics can be expressed, and interpreted, naturally under a constructive definition of mathematical truth.  ...  well-formed formulas of P. 91 By "formula", we shall henceforth mean a "well-formed formula" as defined by Gödel ([Go31a], p11). 92 We follow Gödel's definition of recursive number-theoretic functions and  ... 
arXiv:math/0407529v1 fatcat:igpyvhai7bg4rngg4av65imkq4

Cumulative index volumes 1–100

1992 Theoretical Computer Science  
., The greatest fixed-pointsand rational omega-tree languages 44 (3) ( 1986) 259-274 Takahashi, M., see H.  ...  Rozenberg and R. Verraedt, On inherently ambiguous EOL languages 28 ( l-2) (1984)197-214 Ehrenfeucht, A., M.G. Main and G.  ... 
doi:10.1016/0304-3975(92)90292-n fatcat:ekwes6owtrco3lkfkiqagnketq

The formal roots of Platonism [article]

Bhupinder Singh Anand
2003 arXiv   pre-print
the ability of intuitive truth to faithfully reflect relationships between elements of a Platonic universe, may be as misplaced as an assumption that such truth cannot be expressed in a constructive, and  ...  Of course the integers and rational numbers are also considered reals so one could argue that the cardinality of the reals is aleph 0 or the same as omega.  ...  , non-computational, ambiguous, and essentially Platonic -elements into the standard interpretations of classical mathematics 8 .  ... 
arXiv:math/0305055v2 fatcat:dsdgmxq6ajcbbebzy6hmb5aplm

The Complexity of Infinite Computations In Models of Set Theory

Olivier Finkel, Wolfgang Thomas
2009 Logical Methods in Computer Science  
We prove the following surprising result: there exist a 1-counter B\"uchi automaton and a 2-tape B\"uchi automaton such that the \omega-language of the first and the infinitary rational relation of the  ...  This shows that the topological complexity of an \omega-language accepted by a 1-counter B\"uchi automaton or of an infinitary rational relation accepted by a 2-tape B\"uchi automaton is not determined  ...  are Π 0 2 -sets, and (2) There is a model V 2 of ZFC in which the ω-language L(A) and the infinitary rational relation L(B) are analytic but non Borel sets.  ... 
doi:10.2168/lmcs-5(4:4)2009 fatcat:p5b7skes2bd3nf7qvbnmiygusm
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