Über Darstellungen der elementaren Funktionen II.
Über die darstellbarkeit des syntaktischen monoïdes kontextfreier sprachen
Über die mit Stackautomaten berechenbaren Funktionen.
Über Hilbert's reale und ideale Elemente.
Über rekursive Strukturen.
Un estudio no standard de la teoría de la recursividad relativa.
Una introducción a la W-calculabilidad: Operaciones básicas.
Our purpose is to introduce the W-composition, W-minimalization and W-primitive recursion operations as operations between W-valued functions, where W denotes the ordered semiring ([0,1],+,≤). We prove that: 1) the set of W-calculable functions is closed under the W-composition and W-primitice recursion operations, and 2) the set of the partially W-calculable functions is closed under the W-minimalization operation.
Uncountable suborderings of the isols
Undecidability and Nonperiodicity for Tilings of the Plane.
Undecidability of infinite post correspondence problem for instances of size 8
The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets...
Undecidability of infinite post correspondence problem for instances of size 8
The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets...
Undecidability of infinite post correspondence problem for instances of Size 9
In the infinite Post Correspondence Problem an instance (h,g) consists of two morphisms h and g, and the problem is to determine whether or not there exists an infinite word ω such that h(ω) = g(ω). This problem was shown to be undecidable by Ruohonen (1985) in general. Recently Blondel and Canterini (Theory Comput. Syst.36 (2003) 231–245) showed that this problem is undecidable for domain alphabets of size 105. Here we give a proof that the infinite Post Correspondence Problem is undecidable...
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...
Undecidability vs transfinite induction for the consistency of hyperarithmetical sets.
Undecidable Tiling Problems in the Hyperbolic Plane.
Undecidable varieties with solvable word problems. II.
Undecidable varieties with solvable word problems. III (a semigroup variety).
Une généralisation de la notion d'ensemble immune
Une généralisation des ensembles énumérés