On the Boundedness Property of Semilinear Sets
An additive system to generate a semilinear set is k-bounded if it can generate any element of the set by repeatedly adding vectors according to its rules so that pairwise differences between components in any intermediate vector are bounded by k except for those that have achieved their final target value. We look at two (equivalent) representations of semilinear sets as additive systems: one without states (the usual representation) and the other with states, and investigate their properties concerning boundedness: decidability questions, hierarchies (in terms of k), characterizations, etc.
Keywordssemilinear set generator without states generator with states bounded multitape NFA decidable undecidable
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