Reachability Problem for Polynomial Iteration Is PSPACE-complete
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In the reachability problem for polynomial iteration, we are given a set of polynomials over integers and we are asked whether a particular integer can be reached by a non-deterministic application of polynomials. This model can be seen as a generalisation of vector addition systems. Our main result is that the problem is PSPACE-complete for single variable polynomials. On the other hand, the problem is undecidable for multidimensional polynomials, already starting with three dimensions.
KeywordsReachability problem Polynomial iteration Decidability
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