A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata. B. G. Teubner, Leipzig, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that a structured algorithm might record in its workspace. Walking represents replacing a vertex name by some adjacent vertex found in the input. Jumping represents copying a previously recorded vertex name. Rabin (see [20] Savitch [31] Blum and Sakoda [13] Blum and Kozen [12] Hemmerling [24] and others have considered similar models; see Hemmerling s monograph for an extensive bibliography (going back over a century) emphasizing results for labyrinths graphs embedded in two or three dimensional Euclidean space. The JAG is a structured model, but not a weak one. In particular, ....

....for the problem of undirected graph traversal. The JAG variant we consider is more restricted than the model introduced by Cook and Rackoff, because the pebbles are not permitted to jump. This nonjumping model is closer to the one studied by Blum and Sakoda [13] Blum and Kozen [12] and Hemmerling [24]. We will distinguish this nonjumping variant by referring to it as a WAG walking automaton for graphs . Several authors have considered traversal of undirected regular graphs by a WAG with an unlimited number of states but only the minimum number (one) of pebbles, a model better known as a ....

A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata, volume 114 of Teubner-Texte zur Mathematik. B. G. Teubner Verlagsgesellschaft, Leipzig, 1989.

....that a structured algorithm might record in its workspace. Walking represents replacing a vertex name by some adjacent vertex found in the input. Jumping represents copying a previously recorded vertex name. Rabin (see [24] Savitch [45] Blum and Sakoda [13] Blum and Kozen [12] Hemmerling [30] and others have considered similar models; see Hemmerling s monograph for an extensive bibliography (going back over a century) emphasizing results for labyrinths graphs embedded in two or three dimensional Euclidean space. The JAG is a structured model, but not a weak one. In ....

....powerful; see Section 3. Nevertheless, in a companion paper [9] we prove a lower bound on a model with freely moving pebbles, but without the ability to jump one pebble to another. This nonjumping model is closer to the one studied by Blum and Sakoda [13] Blum and Kozen [12] and Hemmerling [30]. We will distinguish this nonjumping variant by referring to it as a WAG walking automaton for graphs . Following the preliminary appearance of some of these results [10] Edmonds [26] proved a much stronger result for traversing undirected graphs than that proved in [9] and Barnes and ....

A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata, volume 114 of Teubner-Texte zur Mathematik. B. G. Teubner Verlagsgesellschaft, Leipzig, 1989.

....names that a structured algorithm might record in its workspace. Walking represents replacing a vertex name by some adjacent vertex found in the input. Jumping represents copying a previously recorded vertex name. Rabin (see [19] Savitch [33] Blum and Sakoda [9] Blum and Kozen [8] Hemmerling [21] and others have considered similar models; see Hemmerling s monograph for an extensive bibliography (going back over a century) emphasizing results for labyrinths graphs embedded in two or three dimensional Euclidean space. The JAG is a structured model, but not a weak one. In particular, ....

....are surprisingly powerful; see Section 3. Nevertheless, in Section 5 we prove a lower bound on a model with freely moving pebbles, but without the ability to jump one pebble to another. This nonjumping model is closer to the one studied by Blum and Sakoda [9] Blum and Kozen [8] and Hemmerling [21]. We will distinguish this nonjumping variant by referring to it as a WAG walking automaton for graphs . More specifically, using a very different and more complex argument, we prove lower bounds on time that are nonlinear in m for a wide range of values of P . In particular, for any ....

A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata, volume 114 of Teubner-Texte zur Mathematik. B. G. Teubner Verlagsgesellschaft, Leipzig, 1989.

....that the task becomes nearly trivial under those suppositions. Therefore, our point of view corresponds more to labyrinth theory than to computational geometry. Indeed, most of the techniques used in the present paper come from the automaton oriented labyrinth research presented in the monograph [H]. Especially the method of rotation counting (regular swinging) is essentially used in [A] already, where it really shows the power of the compass, whereas the search procedure in [BK] is also based on rudiments of length measuring. 1 The present paper is organized as follows. After introducing ....

....homogeneous environments becomes periodic. Especially, this holds for finite automata, but also for 1 counter and even for pushdown automata. The claim for finite automata can be obtained from Budach s result [B] that no finite automaton can escape from all two dimensional mazes, see also [H]. The self contained proof of the general result is rather lengthy and will be sketched here only. The reader, who is preferably interested in target reaching algorithms, should skip to the next section. The homogeneous environments we will consider here are grids composed of so called ....

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A. Hemmerling. Labyrinth problems -- labyrinth-searching abilities of automata. Teubner--Texte zur Mathematik v. 114, Leipzig 1989.

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A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata. B. G. Teubner, Leipzig, 1989.

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A. Hemmerling. Labyrinth Problems: Labyrinth-Searching Abilities of Automata. B. G. Teubner, Leipzig, 1989.

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