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A tag system is a deterministic computational model published by Emil Leon Post in 1943 as a simple form of Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine (not to be confused with Post-Turing machines)—briefly, a finite state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a fixed number of symbols from the head, and to the tail appends a symbol-string preassigned to the deleted symbol. (Because all of the indicated operations are performed in ''each'' transition, a tag machine strictly has only one state.) == Definition == A ''tag system'' is a triplet (''m'', ''A'', ''P''), where * ''m'' is a positive integer, called the ''deletion number''. * ''A'' is a finite alphabet of symbols, one of which is a special ''halting symbol''. All finite (possibly empty) strings on ''A'' are called ''words''. * ''P'' is a set of ''production rules'', assigning a word ''P(x)'' (called a ''production'') to each symbol ''x'' in ''A''. The production (say ''P(H)'') assigned to the halting symbol is seen below to play no role in computations, but for convenience is taken to be ''P(H)'' = '''H'''. The term ''m-tag system'' is often used to emphasise the deletion number. Definitions vary somewhat in the literature (cf References), the one presented here being that of Rogozhin. * A ''halting word'' is a word that either begins with the halting symbol or whose length is less than ''m''. * A transformation ''t'' (called the ''tag operation'') is defined on the set of non-halting words, such that if ''x'' denotes the leftmost symbol of a word ''S'', then ''t''(''S'') is the result of deleting the leftmost ''m'' symbols of ''S'' and appending the word ''P(x)'' on the right. * A ''computation'' by a tag system is a finite sequence of words produced by iterating the transformation ''t'', starting with an initially given word and halting when a halting word is produced. (By this definition, a computation is not considered to exist unless a halting word is produced in finitely-many iterations. Alternative definitions allow nonhalting computations, for example by using a special subset of the alphabet to identify words that encode output.) The use of a halting symbol in the above definition allows the output of a computation to be encoded in the final word alone, whereas otherwise the output would be encoded in the entire sequence of words produced by iterating the tag operation. A common alternative definition uses no halting symbol and treats all words of length less than ''m'' as halting words. Another definition is the original one used by Post 1943 (described in the historical note below), in which the only halting word is the empty string. 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「Tag system」の詳細全文を読む スポンサード リンク
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