Counterexample generation and representation in model checking for probabilistic timed automata

Recently, probabilistic systems have been widely used. People have drawn attention to counterexample generation for probabilistic system model checking. Current works are mainly focusing on the counterexample generation for Markov chains. Probabilistic timed automata (PTA) is the extension of Markov chain with non-determinism and system clocks. This paper focuses on counterexample representation while model checking PTA. Firstly, the semantic of PTA can be regarded as Markov decision process (MDP); secondly, we use adversary to convert MDP into discrete-time Markov chains (DTMCs); thirdly, we convert DTMCs into weighted graph. So, counterexample generation for PTA can be converted into shortest path problem for weighted digraph. Finally, we use regular expressions to represent the counterexample.