Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate the problem of verifying linear-time properties against inhomogeneous continuous-time Markov chains (ICTMCs). A fundamental question  address is how to compute reachability probabilities.  consider two variants: time-bounded and unbounded reachability. It turns out that both can be characterized as the least solution of a system of integral equations.  show that for the time-bounded case, the obtained integral equations can be transformed into a system of ordinary differential equations; for the time-unbounded case,  identify two sufficient conditions, namely the  eventually periodic assumption  and the  eventually uniform assumption  , under which the problem can be reduced to solving a time-bounded reachability problem for the ICTMCs and a reachability problem for a DTMC. These results provide the basis for a model checking algorithm for LTL. Under the  eventually stable assumption  ,  show how to compute the probability of a set of ICTMC paths which satisfy a given LTL formula. By an automata-based approach,  reduce this problem to the previous established results for reachability problems.
['Taolue Chen', 'Tingting Han', 'Joost-Pieter Katoen', 'Alexandru Mereacre']
I am writing a research paper on a idea LTL Model Checking of Time-Inhomogeneous Markov Chains
[{"from": "human", "value": "I am writing a research paper on a idea LTL Model Checking of Time-Inhomogeneous Markov Chains"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate the problem of verifying linear-time properties against inhomogeneous continuous-time Markov chains (ICTMCs). A fundamental question  address is how to compute reachability probabilities.  consider two variants: time-bounded and unbounded reachability. It turns out that both can be characterized as the least solution of a system of integral equations.  show that for the time-bounded case, the obtained integral equations can be transformed into a system of ordinary differential equations; for the time-unbounded case,  identify two sufficient conditions, namely the  eventually periodic assumption  and the  eventually uniform assumption  , under which the problem can be reduced to solving a time-bounded reachability problem for the ICTMCs and a reachability problem for a DTMC. These results provide the basis for a model checking algorithm for LTL. Under the  eventually stable assumption  ,  show how to compute the probability of a set of ICTMC paths which satisfy a given LTL formula. By an automata-based approach,  reduce this problem to the previous established results for reachability problems."}]