SOLVING DIFFERENCE EQUATIONS IN SEQUENCES: UNIVERSALITY AND UNDECIDABILITY
SOLVING DIFFERENCE EQUATIONS IN SEQUENCES: UNIVERSALITY AND UNDECIDABILITY
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DOI：
10.1017/fms.2020.14
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
G. Pogudin;T. Scanlon;M. Wibmer
中科院分区：
文献类型：
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作者：
G. Pogudin;T. Scanlon;M. Wibmer
我们研究序列环中差分方程解，更一般地，研究由么半群标度的序列环中具有么半群作用的方程的解。例如，该框架包括网格上的差分方程组(例如，标准差分格式)和词上的函数差分方程组。在普适性方面，在基场的基数大于么半群的基数的假设下，我们证明了这类差分方程强零点的一种形式，并构造了一个例子说明这一假设是不可忽略的。在不可判断性方面，我们表明以下问题是不可判断性的：
We study solutions of difference equations in the rings of sequences and, more generally, solutions of equations with a monoid action in the ring of sequences indexed by the monoid. This framework includes, for example, difference equations on grids (for example, standard difference schemes) and difference equations in functions on words. On the universality side, we prove a version of strong Nullstellensatz for such difference equations under the assumption that the cardinality of the ground field is greater than the cardinality of the monoid and construct an example showing that this assumption cannot be omitted. On the undecidability side, we show that the following problems are undecidable: