On intersection problems for polynomially generated sets

Authors:
Wong Karianto;Aloys Krieg;Wolfgang Thomas
Affiliations:
Lehrstuhl für Informatik 7, RWTH Aachen, Germany;Lehrstuhl A für Mathematik, RWTH Aachen, Germany;Lehrstuhl für Informatik 7, RWTH Aachen, Germany
Venue:
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Year:
2006

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Abstract

Some classes of sets of vectors of natural numbers are introduced as generalizations of the semi-linear sets, among them the ‘simple semi-polynomial sets.' Motivated by verification problems that involve arithmetical constraints, we show results on the intersection of such generalized sets with semi-linear sets, singling out cases where the non-emptiness of intersection is decidable. Starting from these initial results, we list some problems on solvability of arithmetical constraints beyond the semi-linear ones