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On Büchi One-Counter Automata

unpublished

In fact, we show that already the equivalence problem for deterministic

fatcat:2pxob5qxnna2fm4acizsqolvzy
*Büchi**one*-*counter**automata*is undecidable. ...*Büchi*pushdown*automata*) is decidable. ... As a second result we show that*on*infinite words universality becomes undecidable*on**Büchi*1-*counter*nets. ...##
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Quasi-Weak Cost Automata: A New Variant of Weakness

2011
*
Foundations of Software Technology and Theoretical Computer Science
*

Cost

doi:10.4230/lipics.fsttcs.2011.66
dblp:conf/fsttcs/KuperbergB11
fatcat:navlbpcpknfurjzvkw5kgpjznq
*automata*have a finite set of*counters*which can be manipulated*on*each transition but do not affect control flow. ... Unlike traditional weak*automata*which have a hard-coded bound*on*the number of alternations between accepting and rejecting states, quasi-weak*automata*bound the alternations using the*counter*values ... It means that performing an increment or a reset*on**counter*i resets all*counters*j below it. Cost*automata*are named B-, S-, or BS-*automata*depending*on*the type(s) of*counters*used. ...##
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Deciding the weak definability of Büchi definable tree languages

2013
*
Annual Conference for Computer Science Logic
*

'11] The boundedness relation ≈ is decidable for

doi:10.4230/lipics.csl.2013.215
dblp:conf/csl/ColcombetKLB13
fatcat:yr2d3x34wrcltgdxus2ftv6yai
*counter*-weak cost*automata*... 70] If there are at least m = |Q U | · |Q V | + 1 blocks*on*every branch in the composed run, then L(U) ∩ L(V) = ∅.Construct weak automaton W such that L(W) = L(V) Given nondeterministic*Büchi**automata*...##
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Highly Undecidable Problems For Infinite Computations

2009
*
RAIRO - Theoretical Informatics and Applications
*

For instance the non-emptiness problem and the infiniteness problem are decidable for ω-languages accepted by

doi:10.1051/ita/2009001
fatcat:m4l7v7vugncgdb2be4wy6ys53a
*Büchi*1-*counter**automata*or even by*Büchi*pushdown*automata*but the non-emptiness problem and ... Notice that*one*cannot infer directly from topological results of [17] that the degrees of decision problems for ω-languages of*Büchi*1-*counter**automata*are the same as the degrees of the corresponding ... So the*counter*value of these*automata*is always zero and they can be seen simply as*Büchi**automata*. ...##
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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 machines like 1-

arXiv:0901.0373v1
fatcat:hto3r4zibjbz7byafrgurbdw5q
*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. ... So the*counter*value of these*automata*is always zero and they can be seen simply as*Büchi**automata*. ...##
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Abstract of PhD Thesis

2014
*
Bulletin of the European Association for Theoretical Computer Science
*

The

dblp:journals/eatcs/Mandrali14
fatcat:xk6tcz7ojvd2rg4cgzcmmyt6ya
*automata*-theoretic approach is*one*of the main ways to develop model checking theories that was originally suggested by Vardi and Wolper in 1986. ... Its core is that each LTL formula ϕ can be represented by a nondeterministic*Büchi*automaton. ... series (a subclass of the class of series accepted by weighted*counter*-free*Büchi**automata*). ...##
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Borel Ranks and Wadge Degrees of Context Free ω-Languages
[chapter]

2005
*
Lecture Notes in Computer Science
*

1-

doi:10.1007/11494645_17
fatcat:xrue3ks7gzhzjl4bcqfxvyiur4
*counter**automata*. ... completely the Borel hierarchy of the class of context free ω-languages, showing that, for each recursive non null ordinal α, there exist some Σ 0 α -complete and some Π 0 α -complete ω-languages accepted by*Büchi*... The class of real time*Büchi*k-*counter**automata*will be denoted r-BC(k). The class of ω-languages accepted by*Büchi*k-*counter**automata*will be denoted BCL(k) ω . ...##
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Incompleteness Theorems, Large Cardinals, and Automata over Infinite Words
[chapter]

2015
*
Lecture Notes in Computer Science
*

We prove that there exist some 1-

doi:10.1007/978-3-662-47666-6_18
fatcat:o7rmf4h6vvasbcueatwt6qmqcy
*counter**Büchi**automata*An for which some elementary properties are independent of theories like Tn =: ZFC + "There exist (at least) n inaccessible cardinals", for integers ... We prove similar results for infinitary rational relations accepted by 2-tape*Büchi**automata*. ... The class of ω-languages accepted by real time*Büchi*k-*counter**automata*will be denoted r-BCL(k) ω . ...##
###
Some problems in automata theory which depend on the models of set theory

2011
*
RAIRO - Theoretical Informatics and Applications
*

We prove that some fairly basic questions

doi:10.1051/ita/2011113
fatcat:dv7hrrq5w5forkchqzlcrh3kx4
*on**automata*reading infinite words depend*on*the models of the axiomatic system ZFC. ...*automata*. ... The class of ω-languages accepted by real time*Büchi*k-*counter**automata*will be denoted r-BCL(k) ω . ...##
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Testability of Oracle Automata
[chapter]

2005
*
Lecture Notes in Computer Science
*

In this paper, we introduce oracle (finite)

doi:10.1007/978-3-540-30500-2_40
fatcat:zkbmv5giurd2jfuucv6ctvnuzu
*automata*that are finite/*Buchi**automata*augmented with oracles in some classes of formal languages. ... Our theory results*on*the testability of oracle*automata*can find applications in the verification of a system containing unspecified/partially specified components. ¤ £ ¦ ¥ § " to the oracle ¥ for a word ... oracle*Buchi**automata*too. ...##
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LTL is closed under topological closure

2014
*
Information Processing Letters
*

Our proof is based

doi:10.1016/j.ipl.2014.03.001
fatcat:3sys5up4jzfw3epdunwyleovpq
*on*constructing a minimal deterministic*counter*-free*Büchi*automaton that recognizes the smallest safety property containing the property expressed by ϕ. ... We then define reduced and*counter*-free*Büchi**automata*, and introduce safety*automata*. ... The family of properties recognized by*Büchi**automata*is the set of ω-regular languages Ω. We next define*counter*-free and reduced*Büchi**automata*. ...##
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On the High Complexity of Petri Nets $$\omega $$-Languages
[chapter]

2020
*
Lecture Notes in Computer Science
*

*Büchi*

*automata*. ... A

*Büchi*k-

*counter*automaton is a 5-tuple The class of ω-languages accepted by real time k-

*counter*

*Büchi*

*automata*(respectively, real time k-blind-

*counter*

*Büchi*

*automata*) is denoted r-CL(k) ω . ... The completeness part follows from the fact that the equivalence and the inclusion problems for ω-languages accepted by real time 1-

*counter*

*Büchi*

*automata*are Π 1 2 -complete [15] , and from the fact ...

##
###
Monitoring Off-the-Shelf Components
[chapter]

2005
*
Lecture Notes in Computer Science
*

*Büchi*

*Automata*. ... Since deterministic Streett

*automata*are more powerful than deterministic

*Büchi*

*automata*, this method is provably more powerful than the

*one*given in [11] . ...

##
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On the topological complexity of ω-languages of non-deterministic Petri nets

2014
*
Information Processing Letters
*

We show that there are Σ 0 3 -complete languages of infinite words accepted by non-deterministic Petri nets with

doi:10.1016/j.ipl.2013.12.007
fatcat:cilait532becthfv2isqnvuw3i
*Büchi*acceptance condition, or equivalently by*Büchi*blind*counter**automata*. ... We show that there exist Σ 0 3complete, hence non ∆ 0 3 , ω-languages accepted by*one*-blind-*counter**Büchi**automata*. ... by*one*-blind-*counter**Büchi**automata*, which are topologically more complex than those accepted by deterministic Petri nets. ...##
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On the Topological Complexity of omega-Languages of Non-Deterministic Petri Nets
[article]

2014
*
arXiv
*
pre-print

We show that there are Σ_3^0-complete languages of infinite words accepted by non-deterministic Petri nets with

arXiv:1401.6835v1
fatcat:mxvhemk7pjdv7c43jhlsa77rse
*Büchi*acceptance condition, or equivalently by*Büchi*blind*counter**automata*. ... We show that there exist Σ 0 3complete, hence non ∆ 0 3 , ω-languages accepted by*one*-blind-*counter**Büchi**automata*. ... by*one*-blind-*counter**Büchi**automata*, which are topologically more complex than those accepted by deterministic Petri nets. ...
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