Veriication of Innnite State Systems by Compositional Model Checking

Compositional model checking methods can be used to reduce the formal veriication of a complex system to model checking problems of tractably small size. However, such techniques are diicult to apply to systems that have large data types, such as memory addresses, or large data arrays such as memories or FIFO buuers. They are also limited to the veriication of systems with xed nite resources. In this paper, a method of compositional veriication is presented that uses the combination of temporal case splitting and data type reductions to reduce types of unbounded range to small nite types, and arrays of unbounded size to small xed-size arrays. The method also supports the use of uninterpreted functions in a novel way, that allows model checking to be applied to systems with uninterpreted functions. These techniques are implemented in a proof assistant that also supports compositional reasoning and reductions via symmetry. Application of the method is illustrated by using this tool to verify an implementation of Tomasulo's algorithm. The use of temporal case splitting, data type reductions and and uninterpreted functions substantially simpliies the proof for xed nite conngurations, and also allows a generic veriication for conngurations of arbitrary word size, arbitrary register le size, arbitrary number of reservation stations and arbitrary number of execution units.