Let L be the set of algebraic integers of a number field Q[gamma]. Let beta L and let A and D be two finite subsets of L wiht 0 D. Assume that beta and all its conjugates have moduli greater than one. Denote by v:A sup *yieus D sup * the normalization relation which maps any representation of an algebraci integer in base beta wiht digits in A onto the ones ofthe same number with digits in D. In this case, the relation v is shown to be computable by a right finite state automaton. If(beta, D) is a valid number system, then the normalization v is a rigth sub-sequential function. We also prove that the question whether (beta,D) does or does not give a valid number system for L can be decided by executing a finite number of arithmetical operations.
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机译：令L为数字字段Qγ的代数整数的集合。令beta L和令A和D为L的两个有限子集，其中D为0D。假定beta及其所有共轭的模量均大于1。用v表示：A sup * yieus D sup *归一化关系，该关系将A中具有基数的beta代数整数的任何表示映射到D中具有数位的同一个数字。在这种情况下，关系v显示为可以由一个正确的有限状态自动机计算。如果（β，D）是有效的数字系统，则归一化v是严格的次序列函数。我们还证明，可以通过执行有限数量的算术运算来确定（β，D）是否给出L的有效数字系统的问题。
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