W.J. Savitch. Relationship between nondeterministic and deterministic tape complexities. Journal on Computer and System Sciences, 4:177--192, 1970. Home/Search Document Not in Database Summary Related Articles Check |
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....O(n ) space. Also, for every M 2 F , M belongs to S if and only if the procedure generates M for some computation path. To test membership of X 2 S, simply run GEN and accept if and only if GEN generates X. This is a nondeterministic polynomial space algorithm. By Savitch s Theorem [Sav70] NPSPACE = PSPACE. Thus, Matrix Semigroup Membership is in PSPACE. To test whether S(A 1 ; A g ) S(B 1 ; B h ) contains a nonzero matrix, run GEN on the two sets of generators independently, and then, accept if and only if both runs generated an identical nonzero matrix. This is ....
W. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4:177-192, 1970.
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....states is limited by n ; hence, the machine can announce that the puzzle is unsolvable after having applied more moves without finding a solution. Since an 6 encoding of an Atomix state needs only polynomial space, it follows that Atomix is in NPSPACE, and, by virtue of Savitch s theorem [Sav70], also in PSPACE. If one could prove that optimal solution lengths for Atomix are bounded by a polynomial of the problem size, it would follow with the same reasoning that Atomix is in NP. Considering that Sokoban, which shows some similarities to Atomix, is PSPACE complete, it doesn t seem ....
W. J. Savitch. Relationships between nondeterministic and deterministic tape complexities. J. Computer and System Sciences, 4(2):177--192, 1970.
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....a choice of several possible transitions. We say the machine accepts if any collection of choices leads to an accepting state. Nondeterministic time and space hierarchies are much trickier to prove because one cannot do straightforward diagonalization on nondeterministic computations. Savitch [Sav70] showed that problems computable in nondeterministic space s(n) are computable in deterministic space s (n) In 1972, Ibarra [Iba72] using translational techniques of Ruby and Fischer [RF65] used Savitch s theorem to show that there exist problems computable in nondeterministic space n but ....
W. Savitch. Relationship between nondeterministic and deterministic tape classes. Journal of Computer and System Sciences, 4:177-192, 1970.
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....further role successors. In such a way, only one branch of the tree model at a time can be generated and investigated by the algorithm, giving rise to a non deterministic procedure consuming only polynomial space and, thus, to PSpace complexity (since NPSpace =PSpace, owing to Savitch s Theorem [24]) In our case, such an optimization does not seem to be possible, since (#) and do not have the tree model property, as number restric tions #p R 1 # #Rm 1 ## #q R 1 # #Rm 1 #Rm (with p q) make some separate (R 1 # #Rm 1 ) role chains merge into confluent (R 1 # #Rm 1 #Rm ) ....
W. J. Savitch. Relationship between Nondeterministic and Deterministic Tape Complexities. Journal of Computer and System Sciences, 4:177--192, 1970.
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