Some fundamental notions of large variable systems
Some problems in automata theory which depend on the models of set theory
We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an ω-language L(x1d49c;) accepted by a Büchi 1-counter automaton x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton x1d49c; such that the cardinality of the complement L(𝒜) − of the ω-language L(𝒜) is not determined...
Some problems in automata theory which depend on the models of set theory
We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an ω-language L(𝒜) accepted by a Büchi 1-counter automaton 𝒜. We prove the following surprising result: there exists a 1-counter Büchi automaton 𝒜 such that the cardinality of the complement L(𝒜) − of the ω-language L(𝒜) is not determined by ZFC: (1) There is a model V1...
Spezielle Gleichungen in freien Halbgruppen und eine Anwendung auf Normalformen regulärer Ereignisse
Syntéza a minimalizace regulárních lineárních generátorů
The isomorphism relation between tree-automatic Structures
An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that...
The recursive sets in certain monadic second order fragments of arithmetic.
The second-order monadic theory of the free inverse monoid is undecidable. (La théorie monadique du second ordre du monoïde inversif libre est indécidable.)
The -calculus alternation-depth hierarchy is strict on binary trees
The μ-calculus alternation-depth hierarchy is strict on binary trees
In this paper we give a simple proof that the alternation-depth hierarchy of the μ-calculus for binary trees is strict. The witnesses for this strictness are the automata that determine whether there is a winning strategy for the parity game played on a tree.
Tree Automata and Automata on Linear Orderings
We show that the inclusion problem is decidable for rational languages of words indexed by scattered countable linear orderings. The method leans on a reduction to the decidability of the monadic second order theory of the infinite binary tree [9].
Über die mit Stackautomaten berechenbaren Funktionen.
Undecidability of topological and arithmetical properties of infinitary rational relations
We prove that for every countable ordinal one cannot decide whether a given infinitary rational relation is in the Borel class (respectively ). Furthermore one cannot decide whether a given infinitary rational relation is a Borel set or a -complete set. We prove some recursive analogues to these properties. In particular one cannot decide whether an infinitary rational relation is an arithmetical set. We then deduce from the proof of these results some other ones, like: one cannot decide whether...
Undecidability of Topological and Arithmetical Properties of Infinitary Rational Relations
We prove that for every countable ordinal α one cannot decide whether a given infinitary rational relation is in the Borel class (respectively ). Furthermore one cannot decide whether a given infinitary rational relation is a Borel set or a -complete set. We prove some recursive analogues to these properties. In particular one cannot decide whether an infinitary rational relation is an arithmetical set. We then deduce from the proof of these results some other ones, like: one cannot decide...
Wadge degrees of -languages of deterministic Turing machines
We describe Wadge degrees of -languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is where is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].
Wadge Degrees of ω-Languages of Deterministic Turing Machines
We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξω where ξ = ω1CK is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].
Weakly maximal decidable structures
We prove that there exists a structure M whose monadic second order theory is decidable, and such that the first-order theory of every expansion of M by a constant is undecidable.
Zur Beweistheorie der Kripke-Platek-Mengenlehre über den natürlichen Zahlen.
Алгоритмическая природа инвариантных свойств грамматик непосредственно составляющих
Верхняя оценка конечноавтоматной сложности для одного класса порождающих схем с операциями дополнения и пересечения