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A symmetric Turing machine is a Turing machine which has a configuration graph that is undirected (that is, configuration i yields configuration j if and only if j yields i). == Definition of Symmetric Turing machines == Formally, we define a variant of Turing machines with a set of transitions of the form ''(p,ab,D,cd,q)'', where ''p,q'' are states, ''ab,cd'' are pairs of symbols and ''D'' is a direction. If ''D'' is ''left'', then the head of a machine in state ''p'' above a tape symbol ''b'' preceded by a symbol ''a'' can be transitioned by moving the head left, changing the state to ''q'' and replacing the symbol ''a,b'' by ''c,d''. The opposite transition ''(q,cd,-D,ab,q)'' can always be applied. If ''D'' is right the transition is analogous. The ability to peek at two symbols and change both at a time is non-essential, but makes the definition easier. Such machines were first defined in 1982 by Lewis and Papadimitriou,〔Jesper Jansson. (Deterministic Space-Bounded Graph Connectivity Algorithms ). Manuscript. 1998.〕〔Harry R. Lewis and Christos H. Papadimitriou. Symmetric space-bounded computation. ''Theoretical Computer Science''. pp.161-187. 1982.〕 who were looking for a class in which to place USTCON, the problem asking whether there is a path between two given vertices s,t in an undirected graph. Until this time, it could be placed only in NL, despite seeming not to require nondeterminism (the asymmetric variant STCON was known to be complete for NL). Symmetric Turing machines are a kind of Turing machines with limited nondeterministic power, and were shown to be at least as powerful as deterministic Turing machines, giving an interesting case in between. STIME(T(n)) is the class of the languages accepted by a symmetric Turing machine running in time O(T(n)). It can easily proved that STIME(T)=NTIME(T) by limiting the nondeterminism of any machine in NTIME(T) to an initial stage where a string of symbols is nondeterministically written, followed by deterministic computations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Symmetric Turing machine」の詳細全文を読む スポンサード リンク
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