Efficient Solving of Time-dependent Answer Set Programs

Answer set programs with time predicates are useful to model systems whose properties depend on time, like for example gene regulatory networks. A state of such a system at time point t then corresponds to the literals of an answer set that are grounded with time constant t. An important task when modelling time-dependent systems is to find steady states from which the system's behaviour does not change anymore. This task is complicated by the fact that it is typically not known in advance at what time steps these steady states occur. A brute force approach of estimating a time upper bound tmax and grounding and solving the program w.r.t. that upper bound leads to a suboptimal solving time when the estimate is too low or too high. In this paper we propose a more efficient algorithm for solving Markovian programs, which are time-dependent programs for which the next state depends only on the previous state. Instead of solving these Markovian programs for a long time interval {0,...,tmax}, we successively find answer sets of parts of the grounded program. Our approach guarantees the discovery of all steady states and cycles while avoiding unnecessary extra work.