Model-Generation of a Fictitious Clock Real-Time Logic Using Sharing Trees

Abstract

We present first the logic mtl, a real-time temporal logic that is at the heart of the real-time specification language Albert. Since this logic is undecidable, we approximate it (using the theory of Abstract Interpretation) by its fictitious clock counterpart, MTLfc.We then present a symbolic tableau-based model generation decision procedure in ECLFC, which is theoretically optimal. In practice however, we see that the introduction of integer-valued prophecy variables will make it more efficient. From these variables, we reconstruct by reverting the process a logic that we call ExpSpace, which can be decided in PSpace, and has the same expressivity as MTLfc. Theory thus shows that memory space is the critical factor. However, the classical compaction of memory space by BDDs is not ideal here, since our integer variables would need to be encoded by booleans. Therefore, we use Sharing Trees instead, a compact data structure that can accommodate arbitrary data types. Preliminary results on this implementation are reported.