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  1.  6
    Characterizations of the classΔta2 Over Euclidean Spaces.Armin Hemmerling - 2004 - Mathematical Logic Quarterly 50 (45):507-519.
    We present some characterizations of the members of Δta2, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces ℝk. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of Δta2. Effective difference chains of transfinite order types, consisting of complements of effectively exhaustible sets, as well as (...)
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  2.  15
    Characterizations of the Class ~2^T^a Over Euclidean Spaces.Armin Hemmerling - 2004 - Mathematical Logic Quarterly 50 (4):507.
    We present some characterizations of the members of Δta2, that class of the topological arithmetical hierarchy which is just large enough to include several fundamental types of sets of points in Euclidean spaces ℝk. The limit characterization serves as a basic tool in further investigations. The characterization by effective difference chains of effectively exhaustible sets yields only a hierarchy within a subfield of Δta2. Effective difference chains of transfinite order types, consisting of complements of effectively exhaustible sets, as well as (...)
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  3.  43
    Navigation Without Perception of Coordinates and Distances.Armin Hemmerling - 1994 - Mathematical Logic Quarterly 40 (2):237-260.
    We consider the target-reaching problem in plane scenes for a point robot which has a tactile sensor and can locate the target ray. It might have a compass, too, but it is not able to perceive the coordinates of its position nor to measure distances. The complexity of an algorithm is measured by the number of straight moves until reaching the target, as a function of the number of vertices of the scene. It is shown how the target point can (...)
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  4.  3
    Letter From the Outgoing Managing Editor/Letter From the New Managing Editor.Günter Asser & Armin Hemmerling - 2005 - Mathematical Logic Quarterly 51 (1):3-4.
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  5.  13
    Computability of String Functions Over Algebraic Structures Armin Hemmerling.Armin Hemmerling - 1998 - Mathematical Logic Quarterly 44 (1):1-44.
    We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a BSS-like (...)
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  6.  4
    Approximate Decidability in Euclidean Spaces.Armin Hemmerling - 2003 - Mathematical Logic Quarterly 49 (1):34-56.
    We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by computability of the (...)
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  7.  6
    On P Versus NP for Parameter‐Free Programs Over Algebraic Structures.Armin Hemmerling - 2001 - Mathematical Logic Quarterly 47 (1):67-92.
    Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures.
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  8.  7
    Computability Over Structures of Infinite Signature.Armin Hemmerling - 1998 - Mathematical Logic Quarterly 44 (3):394-416.
    Continuing the paper [7], in which the Blum-Shub-Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. Such structures even have universal functions satisfying (...)
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  9.  30
    The Hausdorff-Ershov Hierarchy in Euclidean Spaces.Armin Hemmerling - 2005 - Archive for Mathematical Logic 45 (3):323-350.
    The topological arithmetical hierarchy is the effective version of the Borel hierarchy. Its class Δta 2 is just large enough to include several types of pointsets in Euclidean spaces ℝ k which are fundamental in computable analysis. As a crossbreed of Hausdorff's difference hierarchy in the Borel class ΔB 2 and Ershov's hierarchy in the class Δ0 2 of the arithmetical hierarchy, the Hausdorff-Ershov hierarchy introduced in this paper gives a powerful classification within Δta 2. This is based on suitable (...)
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  10.  19
    1-Pointer Automata Searching Finite Plane Graphs.Armin Hemmerling - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (13-16):245-256.
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  11.  17
    Pebble Automata in Labyrinths with Rotation Systems.Armin Hemmerling - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (26-30):453-466.
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  12.  16
    Zur Raumkompliziertheit Mehrdimensionaler Turing-Automaten.Armin Hemmerling & Gerd Murawski - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (13-16):233-258.
  13.  12
    Editorial: MLQ – Math. Log. Quart. 1/2006.Armin Hemmerling - 2006 - Mathematical Logic Quarterly 52 (1):3-3.
    I hope you have had no trouble identifying this issue of our journal, even if the cover has been changed slightly. I would like to draw your attention to a more essential improvement in the journal's affairs: namely, that the Editorial Board has been enlarged by four new members. These are the following: Douglas Bridges , Ulrich Kohlenbach , H. Dugald Macpherson , and Pavel Pudlak . Please don't hesitate to contact a fellow editor, in particular the managing editor, if (...)
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  14.  9
    Editorial: Math. Log. Quart. 2/2008.Armin Hemmerling - 2008 - Mathematical Logic Quarterly 54 (2):128-128.
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  15.  7
    The Discrete Parts of Approximately Decidable Sets in Euclidean Spaces.Armin Hemmerling - 2003 - Mathematical Logic Quarterly 49 (4):428.
    It is shown that the classes of discrete parts, A ∩ ℕk, of approximately resp. weakly decidable subsets of Euclidean spaces, A ⊆ ℝk, coincide and are equal to the class of ω-r. e. sets which is well-known as the first transfinite level in Ershov's hierarchy exhausting Δ02.
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  16.  6
    Günter Asser.Armin Hemmerling - 2015 - Mathematical Logic Quarterly 61 (3):127-131.
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  17.  4
    1‐Pointer Automata Searching Finite Plane Graphs.Armin Hemmerling - 1986 - Mathematical Logic Quarterly 32 (13‐16):245-256.
  18.  5
    Pebble Automata in Labyrinths with Rotation Systems.Armin Hemmerling - 1991 - Mathematical Logic Quarterly 37 (26‐30):453-466.
  19.  2
    Zur Raumkompliziertheit Mehrdimensionaler Turing‐Automaten.Armin Hemmerling & Gerd Murawski - 1984 - Mathematical Logic Quarterly 30 (13‐16):233-258.
  20. Editorial: Math. Log. Quart. 1/2007.Armin Hemmerling - 2007 - Mathematical Logic Quarterly 53 (1):3-3.
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