The central notion in a replacement system is one of a transformation on a set of objects. Starting with a given object, in one ″move″ it is possible to reach one of a set of objects. An object from which no move is possible is called irreducible. A replacement system is Church-Rosser if starting with any object a unique irreducible object is reached. A generalization of the above notion is a replacement system consisting of a set of objects (S), a transformation, and an equivalence relation on S. A replacement system is Church-Rosser if starting with objects equivalent under an equivalence relation on S, equivalent irreducible objects are reached. Necessary and sufficient conditions are determined that simplify the task of testing if a replacement system is Church-Rosser. Attention will be paid to showing that a replacement system is Church-Rosser using information about parts of the system.
|Original language||English (US)|
|Title of host publication||J Assoc Comput Mach|
|Number of pages||9|
|Publication status||Published - Oct 1974|
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