On the Complexity of Computing Minimal Unsatisfiable LTL formulas

We show that (1) the Minimal False QCNF search-problem (MF-search) and the Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE complete because of the very expressive power of QBF/LTL, (2) we extend the PSPACE-hardness of the MF decision problem to the MU decision problem. As a consequence, we deduce a positive answer to the open question of PSPACE hardness of the inherent Vacuity Checking problem. We even show that the Inherent Non Vacuous formula search problem is also FPSPACE-complete.Comment: Minimal unsatisfiable cores For LTL causes inherent vacuity checking redundancy coverag

Handling Conflicts in Depth-First Search for LTL Tableau to Debug Compliance Based Languages

Providing adequate tools to tackle the problem of inconsistent compliance rules is a critical research topic. This problem is of paramount importance to achieve automatic support for early declarative design and to support evolution of rules in contract-based or service-based systems. In this paper we investigate the problem of extracting temporal unsatisfiable cores in order to detect the inconsistent part of a specification. We extend conflict-driven SAT-solver to provide a new conflict-driven depth-first-search solver for temporal logic. We use this solver to compute LTL unsatisfiable cores without re-exploring the history of the solver.Comment: In Proceedings FLACOS 2011, arXiv:1109.239