Computing minimal unsatisfiable core for LTL over finite traces

Abstract

Abstract In this paper, we consider the minimal unsatisfiable core (MUC) problem for linear temporal logic over finite traces (LTL$_{f}$), which nowadays is a popular formal-specification language for AI-related systems. Efficient algorithms to compute such MUCs can help locate the inconsistency rapidly in the written LTL$_{f}$ specification and are very useful for the system designers to amend the flawed requirement. As far as we know, there are no available tools off-the-shelf so far that provide MUC computation for LTL$_{f}$. We present here two generic approaches NaiveMUC and BinaryMUC to compute an MUC for LTL$_{f}$. Moreover, we introduce heuristics that are based on the Boolean unsatisfiable core (UC) technique to accelerate the two approaches, which are named NaiveMUC+UC and BinaryMUC+UC, respectively. In particular, for global LTL$_{f}$ formulas, we show that the MUC computation can be reduced to the pure Boolean MUC computation, which therefore conducts the GlobalMUC approach. Our experiments show that GlobalMUC performs the best to compute an MUC for global formulas, and BinaryMUC+UC is the best for an arbitrary unsatisfiable formula.