This paper resolves two open problems on linear integer arithmetic (LIA), also known as Presburger arithmetic. First, we give a triply exponential geometric decision procedure for LIA, i.e., a procedure based on manipulating semilinear sets. This ...

Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as bounded ness, reach ability, regularity, as well as context-...

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study ...

We prove completeness results for twenty-three problems in semilinear geometry. These results involve semilinear sets given by additive circuits as input data. If arbitrary real constants are allowed in the circuit, the completeness results are for the ...

We consider the model of population protocols introduced by Angluin et al. [2], in which anonymous finite-state agents stably compute a predicate of their inputs via two-way interactions in the all-pairs family of communication networks. We prove that ...