Counting Constraints in Flat Array Fragments
  We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a fragment and we implement our algorithms. The experiments run in discharging proof obligations coming from invariant checking and bounded model-checking benchmarks show the practical feasibility of our decision procedure. 
Francesco Alberti and Silvio Ghilardi and Elena Pagani
cs.LO