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On Büchi One-Counter Automata

Stanislav Böhm, Stefan Göller, Simon Halfon, Piotr Hofman
unpublished
In fact, we show that already the equivalence problem for deterministic 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.  ... 
fatcat:2pxob5qxnna2fm4acizsqolvzy

Quasi-Weak Cost Automata: A New Variant of Weakness

Denis Kuperberg, Michael Vanden Boom, Marc Herbstritt
2011 Foundations of Software Technology and Theoretical Computer Science  
Cost 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.  ... 
doi:10.4230/lipics.fsttcs.2011.66 dblp:conf/fsttcs/KuperbergB11 fatcat:navlbpcpknfurjzvkw5kgpjznq

Deciding the weak definability of Büchi definable tree languages

Thomas Colcombet, Denis Kuperberg, Christof Löding, Michael Vanden Boom, Marc Herbstritt
2013 Annual Conference for Computer Science Logic  
'11] The boundedness relation ≈ is decidable for 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  ... 
doi:10.4230/lipics.csl.2013.215 dblp:conf/csl/ColcombetKLB13 fatcat:yr2d3x34wrcltgdxus2ftv6yai

Highly Undecidable Problems For Infinite Computations

Olivier Finkel
2009 RAIRO - Theoretical Informatics and Applications  
For instance the non-emptiness problem and the infiniteness problem are decidable for ω-languages accepted by 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.  ... 
doi:10.1051/ita/2009001 fatcat:m4l7v7vugncgdb2be4wy6ys53a

Highly Undecidable Problems For Infinite Computations [article]

Olivier Finkel
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-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.  ... 
arXiv:0901.0373v1 fatcat:hto3r4zibjbz7byafrgurbdw5q

Abstract of PhD Thesis

Eleni Mandrali
2014 Bulletin of the European Association for Theoretical Computer Science  
The 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).  ... 
dblp:journals/eatcs/Mandrali14 fatcat:xk6tcz7ojvd2rg4cgzcmmyt6ya

Borel Ranks and Wadge Degrees of Context Free ω-Languages [chapter]

Olivier Finkel
2005 Lecture Notes in Computer Science  
1-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 .  ... 
doi:10.1007/11494645_17 fatcat:xrue3ks7gzhzjl4bcqfxvyiur4

Incompleteness Theorems, Large Cardinals, and Automata over Infinite Words [chapter]

Olivier Finkel
2015 Lecture Notes in Computer Science  
We prove that there exist some 1-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 .  ... 
doi:10.1007/978-3-662-47666-6_18 fatcat:o7rmf4h6vvasbcueatwt6qmqcy

Some problems in automata theory which depend on the models of set theory

Olivier Finkel
2011 RAIRO - Theoretical Informatics and Applications  
We prove that some fairly basic questions 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 .  ... 
doi:10.1051/ita/2011113 fatcat:dv7hrrq5w5forkchqzlcrh3kx4

Testability of Oracle Automata [chapter]

Gaoyan Xie, Cheng Li, Zhe Dang
2005 Lecture Notes in Computer Science  
In this paper, we introduce oracle (finite) 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.  ... 
doi:10.1007/978-3-540-30500-2_40 fatcat:zkbmv5giurd2jfuucv6ctvnuzu

LTL is closed under topological closure

Grgur Petric Maretić, Mohammad Torabi Dashti, David Basin
2014 Information Processing Letters  
Our proof is based 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.  ... 
doi:10.1016/j.ipl.2014.03.001 fatcat:3sys5up4jzfw3epdunwyleovpq

On the High Complexity of Petri Nets $$\omega $$-Languages [chapter]

Olivier Finkel
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  ... 
doi:10.1007/978-3-030-51831-8_4 fatcat:3kxxriteq5ewropgozkc2vfnmu

Monitoring Off-the-Shelf Components [chapter]

A. Prasad Sistla, Min Zhou, Lenore D. Zuck
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] .  ... 
doi:10.1007/11609773_15 fatcat:q7yw2urlwfbydg744cza2t2cd4

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

Olivier Finkel, Michał Skrzypczak
2014 Information Processing Letters  
We show that there are Σ 0 3 -complete languages of infinite words accepted by non-deterministic Petri nets with 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.  ... 
doi:10.1016/j.ipl.2013.12.007 fatcat:cilait532becthfv2isqnvuw3i

On the Topological Complexity of omega-Languages of Non-Deterministic Petri Nets [article]

Olivier Finkel, Michał Skrzypczak
2014 arXiv   pre-print
We show that there are Σ_3^0-complete languages of infinite words accepted by non-deterministic Petri nets with 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.  ... 
arXiv:1401.6835v1 fatcat:mxvhemk7pjdv7c43jhlsa77rse
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