W. Savitch. Maze recognizing automata and nondeterministic tape complexity. JCSS, 7:389-403, 1973.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with the same space bound. It is straightforward to check that L NL P, and these three classes are thought to be distinct. There are a number of nontrivial problems solvable in L (for example see [LZ77] as well as problems known to be in NL which are not believed to be in L (for example see [Sav73, Jon75] Numerous problems in P are thought to lie outside of L or NL. For example, one such problem is the circuit value problem, the problem of determining the value of a Boolean circuit, given inputs to the circuit. The circuit value problem is one of many problems in P which is known to be ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. JCSS, 7:389-403, 1973.

....other pebble reaches them. The pebbles represent vertex 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 [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 ....

....for graph traversal. For instance, a JAG can execute a depth first or breadth first search, provided it has one pebble for each vertex, by leaving a pebble on each visited vertex in order to avoid revisiting it, and keeping the stack or queue of pebble names in its state. Furthermore, as Savitch [31] shows, a JAG with the additional power to move a pebble from vertex i to vertex i 1 can simulate an arbitrary Turing machine on directed graphs. Even without this extra feature, we have shown [10] that JAGs are as powerful as Turing machines for the purposes of solving undirected graph problems ....

W. J. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7(4):389--403, 1973.

....vertices s; t 2 V , the s t connectivity problem asks whether there is a directed path from s to t in G, i.e. whether a sequence of directed edges (s; u 1 ) u 1 ; u 2 ) u k ; t) exists. The s t connectivity problem is well known to be complete for NL under logspace many one reductions [Sav73]. Immerman [Imm87] has shown that this problem is complete for NL under an extremely weak form of many one reductions called first order projections (that are, in fact, quantifier free) We note that the s t connectivity problem remains NL complete even when restricted to directed acyclic graphs. ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7:389--403, 1973.

.... in NL we have that TC is complete for NL via quanti er free rst order translations with successor (clearly, we may have other translations such as rst order translations with, or without, successor) Such a result sharpens the well known result that TC is complete for NL via log space reductions [29]. An important point to note is that adopting such a logical viewpoint to complexity theory yields techniques for proving problems complete for some complexity class that were hitherto unavailable (see [34] and scope for showing that traditional complete problems might not remain complete under ....

W. Savitch, Maze recognizing automata and nondeterministic tape complexity, J. Comput. System Sci. 7 (1973) 389-403.

....answered the questions (Q1 0 ) and (Q2 0 ) but have provided evidence that their answers are negative by proving NNJAG lower bounds on the space and time space tradeoff. In Chapter 2, we introduce the NNJAG (Node named JAG) model which is a generalization of the JAG model. It follows from [Sav73] that if we further allow an NNJAG to perform the strong jumping operations, then the resulting machine is as powerful as a branching program for solving graph theoretic problems. Hence the NNJAG model seems to be a suitable intermediate model between the JAG model 5 and a general computation ....

....G, if H can be solved by a nondeterministic Turing machine in time T (n) and space S(n) simultaneously, then it can also be solved by a nondeterministic NNJAG in time O(nT (n) and space O(S(n) log n) simultaneously provided a pebble is placed on node s initially. Proof: It is shown in Savitch [Sav73] that a nondeterministic JAG with strong jumping can simulate an arbitrary nondeterministic Turing machine efficiently. A strong jump in a JAG is a move of the form: jump pebble P from its current node u, say, to node u 1modn and assume state Q. It suffices to show how to simulate a strong ....

W. J. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7(4):389--403, 1973.

....s; t 2V , the s t connectivity problem asks whether there is a directed path from s to t in G, i.e. whether a sequence of directed edges (s; u 1 ) u 1 ; u 2 ) u k ; t) exists. The s t connectivity problem is well known to be complete for NL under logspace many one reductions [Sav73] Immerman [Imm87] has shown that this problem is complete for NL under an extremely weak form of many one reductions called quantifier free firstorder projections. We note that the s t connectivity problem is complete for NL (under logspace or even NC 1 computable) many one reductions, even ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. J. Comp. Sys. Sci., 7:389--403, 1973.

....s; t 2 V , the s t connectivity problem asks whether there is a directed path from s to t in G, i.e. whether a sequence of directed edges (s; u 1 ) u 1 ; u 2 ) u k ; t) exists. The s t connectivity problem is well known to be complete for NL under logspace many one reductions [Sav73]. Immerman [Imm87] has shown that this problem is complete for NL under an extremely weak form of many one reductions called first order projections (that are, in fact, quantifier free) We note that the s t connectivity problem is complete for NL (under logspace or even NC 1 computable) ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. J. Comp. Sys. Sci., 7:389--403, 1973.

....other pebble reaches them. The pebbles represent vertex 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 [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 ....

....graph traversal. For instance, a JAG can execute a depth first or breadth first search, provided it has one pebble for each vertex, by leaving a pebble on each visited vertex in order to avoid revisiting it, and keeping the stack or queue of pebble names in its state. Furthermore, as Savitch [45] shows, a JAG with the additional power to move a pebble from vertex i to vertex i 1 can simulate an arbitrary Turing machine on directed graphs. Even without this extra feature, we will show in Section 3 that JAGs are as powerful as Turing machines for the purposes of solving undirected graph ....

W. J. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7(4):389--403, 1973.

....acyclic graphs, DAG STCON for short, consists of the description of a directed acyclic graph G and two of its vertices s and t. The instance hG; s; ti belongs to DAG STCON if there is a directed path in G from vertex s to vertex t. DAG STCON is complete for NL under logspace many one reductions [23] and actually even under NC 1 computable many one reductions. 5 We denote the analogous problem for undirected acyclic graphs by F STCON ( F for forest) It is complete for L under NC 1 computable many one reductions [9] We use the following notation introduced by Nisan [18] RP ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7:389--403, 1973.

.... on learning unknown graphs under various conditions (e.g. BRS93] DP90] RS87] RS93] Rabin proposed the idea of dropping pebbles to mark nodes [Rab67] This suggestion led to work exploring the searching capabilities of a finite automaton supplied with pebbles (e.g. BS77] BK78] Sav72] Cook and Rackoff generalized the idea of pebbles to jumping automata [CR80] However, most previous work has concentrated on learning undirected graphs or graphs with distinguishable nodes. The power behind the two robot model lies in the robots abilities to recognize each other and to move ....

Walter J. Savitch. Maze recognizing automata and nondeterministic tape complexity. JCSS, 7:389--403, 1972.

....acyclic graphs, DAG STCON for short, consists of the description of a directed acyclic graph G and two of its vertices s and t. The instance hG; s; ti belongs to DAG STCON if there is a directed path in G from vertex s to vertex t. DAG STCON is complete for NL under logspace many one reductions [30] and actually even under NC 1 computable many one reductions. We denote the analogous problem for undirected acyclic graphs by F STCON (iFj for forest) It is complete for L under NC 1 computable many one reductions [11] We use the following notation introduced by Nisan [25] RP ....

W. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7:389403, 1973.

....[BK78] improve this result to show that a single automaton with 2 pebbles can search a finite, 2 dimensional maze. Their results imply that mazes are strictly easier to search than planar graphs, since they also show that no single automaton with pebbles can search all planar graphs. Savitch [Sav73] introduces the notion of a maze recognizing automaton (MRA) which is a DFA with a finite number of distinguishable pebbles. The mazes in Savitch s paper are n node 2 regular graphs, and the MRAs have the added ability to jump to the node with the next higher or lower number in some ordering. ....

Walter J. Savitch. Maze recognizing automata and nondeterministic tape complexity. JCSS, 7:389--403, 1973.

....other pebble reaches them. The pebbles represent vertex 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 ....

....graph traversal. For instance, a JAG can execute a depth first or breadth first search, provided it has one pebble for each vertex, by leaving a pebble on each visited vertex in order to avoid revisiting it, and keeping the stack or queue of pebble names in its state. Furthermore, as Savitch shows [33], a JAG with the additional power to move a pebble from vertex i to vertex i 1 can simulate an arbitrary Turing machine on directed graphs. Even without this extra feature, we will show in Section 3 that JAGs are as powerful as Turing machines for the purposes of solving undirected graph ....

W. J. Savitch. Maze recognizing automata and nondeterministic tape complexity. Journal of Computer and System Sciences, 7(4):389--403, 1973.

No context found.

<F3.734e+05> W. J.<F3.811e+05> Savitch,<F3.365e+05> Maze recognizing automata and nondeterministic tape<F3.811e+05> complexity, J. Comput. System Sci., 7 (1973), pp. 389--403.

No context found.

W. Savitch, "Maze Recognizing Automata and Nondeterministic Tape Complexity," JCSS 7, 1973, (389-403).

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