Adding Monotonic Counters to Automata and Transition Graphs

We analyze models of infinite-state automata extended by monotonic counting mechanisms, starting from the (finite-state) Parikh automata studied by Klaedtke and Rueß. We show that, for linearbounded automata, this extension does not increase the language recognition power. In the framework of infinite transition systems developed by Caucal and others, we show that adding monotonic counters to synchronized rational graphs still results in synchronized rational graphs, in contrast to the case of pushdown graphs or prefix-recognizable graphs. For prefix-recognizable graphs, however, we show that the extension by monotonic counters retains the decidability of the reachability problem.