Transformations on Dependency Graphs :

Dependency graphs are used to model data and control ow in hardware and software design. In a transformational design approach, optimization and re nement transformations are used to transform dependency-graph-based speci cations at higher abstraction levels to those at lower abstraction levels. In this dissertation, we investigate the formal speci cation and mechanical veri cation of transformations on dependency graphs. Among formal methods, the axiomatic method provides a mechanism to specify an object by asserting properties it should satisfy. We show that an axiomatic speci cation coupled with an e cient mechanical veri cation is the most suitable formal approach to address the veri cation of transformations on dependency graphs. We have provided a formal speci cation of dependency graphs, and veri ed the correctness of a variety of transformations used in an industrial synthesis framework. Errors have been discovered in the transformations, and modi cations have been proposed and incorporated. Further, the formal speci cation has permitted us to examine the generalization and composition of transformations. In the process, we have discovered new transformations that could be used for further optimization and re nement than were possible before. We have devised an e cient veri cation scheme that integrates model-checking and theorem-proving, the two major techniques for formal veri cation, in a seamless manner. First, we focus on the dependency graph formalism used in the high-level synthesis system part of the SPRITE project at Philips Research Labs. The transformations in the synthesis system are used for re nement and optimization of descriptions speci ed in a dependency graph language called SPRITE Input Language (SIL). SIL is an intermediate language used during the synthesis of hardware described using languages such as VHDL, SILAGE and ELLA. Besides being an intermediate language, it forms the backbone of the TRADES synthesis system of the University of Twente. SIL has been used in the design of hardware for audio and video applications. Next, we present schemes for seamless integration of theorem-proving and modelchecking for e cient veri cation. We use the Prototype Veri cation System (PVS) to specify and verify the correctness of the transformations. The PVS speci cation language, based on typed higher order logic allows us to investigate the correctness using a convenient level of abstraction. The PVS veri er features automatic procedures and interactive veri cation rules to check properties of speci cations. We have integrated e cient simpli ers and model-checkers with PVS to facilitate veri cation. Finally, we show how our method can be applied in the study of formalisms for hybrid/real-time systems, optimizing compilers, dataow languages, and software iii engineering. Based on the applications of our method on such o -the-shelf formalisms, we substantiate our claim that an axiomatic speci cation coupled with an e cient mechanical veri cation is the most suitable approach to specify and verify transformations on dependency graphs independent of underlying behavior models. iv