No abstract

Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finite-state abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of hybrid systems. Following an approach originally developed for finite-state systems [11, 25], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. Examples illustrate our counterexample-guided refinement procedure. Experimental results for a prototype implementation indicate significant advantages over existing methods.

The completion of meiosis requires the spatial and temporal coordination of cytokinesis and karyokinesis. During meiotic maturation, many events, such as formation, location, and rotation of the meiotic spindle as well as chromosomal movement, polar body extrusion, and pronuclear migration, are dependent on regulation of the cytoskeleton system. To study functions of microfilaments in meiosis, we induced metaphase II (MII) mouse oocytes to resume meiosis by in vitro fertilization or parthenogenetic activation, and we treated such oocytes with cytochalasin B (CB). The changes of the meiotic spindle, as visualized in preparations stained for beta-tubulin and chromatin, were observed by fluorescent confocal microscopy. The meiotic spindle of MII oocytes was observed to be parallel to the plasmalemma. After meiosis had resumed, the spindle rotated to the vertical position so that the second polar body could be extruded into the perivitelline space. When meiosis resumed and oocytes were treated with 10 micro g/ml of CB, the spindle rotation was inhibited. Consequently, the oocyte formed an extra pronucleus instead of extruding a second polar body. These results indicate that spindle rotation is essential for polar body extrusion; it is the microfilaments that play a crucial role in regulating rotation of the meiotic spindle.

Abstract. Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finite-state abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of infinite-state systems, in particular of hybrid systems. Following an approach originally developed for finite-state systems [1, 2], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. A detailed example illustrates our counterexample-guided refinement procedure. Experimental results for a prototype implementation of the procedure indicate its advantages over existing methods.