Abstract. Constrained graphs are directed graphs describing the control flow of processes models. In such graphs, nodes represent activities involved in the process, and edges the precedence relationship among such activities. Typically, nodes and edges can specify some constraints, which control the interaction among the activities. Faced with the above features constrained graphs are widely used in the modelling and analysis of Workflow processes. In this paper we overview two mining problems related to the analysis of constrained graphs, namely the analysis of frequent patterns of execution, and the induction of a constrained graph from a set of execution traces. We discuss some complexity aspects related to the problem of reasoning and mining on constrained graphs, and overview two algorithms for the mentioned problems.