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- OBDDs (2) (remove)

Today, usage of complex circuit designs in computers, in multimedia applications and communication devices is widespread and still increasing. At the same time, due to Moore's Law we do not expect to see an end in the growth of the complexity of digital circuits. The decreasing ability of common validation techniques -- like simulation -- to assure correctness of a circuit design enlarges the need for formal verification techniques. Formal verification delivers a mathematical proof that a given implementation of a design fulfills its specification. One of the basic and during the last years widely used data structure in formal verification are the so called Ordered Binary Decision Diagrams (OBDDs) introduced by R. Bryant in 1986. The topic of this thesis is integration of structural high-level information in the OBDD-based formal verification of sequential systems. This work consist of three major parts, covering different layers of formal verification applications: At the application layer, an assertion checking methodology, integrated in the verification flow of the high-level design and verification tool Protocol Compiler is presented. At the algorithmic layer, new approaches for partitioning of transition relations of complex finite state machines, that significantly improve the performance of OBDD-based sequential verification are introduced. Finally, at the data structure level, dynamic variable reordering techniques that drastically reduce the time required for reordering without a trade-off in OBDD-size are described. Overall, this work demonstrates how a tighter integration of applications by using structural information can significantly improve the efficiency of formal verification applications in an industrial setting.

Hardware bugs can be extremely expensive, financially. Because microprocessors and integrated circuits have become omnipresent in our daily live and also because of their continously growing complexity, research is driven towards methods and tools that are supposed to provide higher reliability of hardware designs and their implementations. Over the last decade Ordered Binary Decision Diagrams (OBDDs) have been well proven to serve as a data structure for the representation of combinatorial or sequential circuits. Their conciseness and their efficient algorithmic properties are responsible for their huge success in formal verification. But, due to Shannon's counting argument, OBDDs can not always guarantee the concise representation of a given design. In this thesis, Parity Ordered Binary Decision Diagrams are presented, which are a true extension of OBDDs. In addition to the regular branching nodes of an OBDD, functional nodes representing a parity operation are integrated into the data structure, thus resulting in Parity-OBDDs. Parity-OBDDs are more powerful than OBDDs are, but, they are no longer a canonical representation. Besides theoretical aspects of Parity-OBDDs, algorithms for their efficient manipulation are the main focus of this thesis. Furthermore, an analysis on the factors that influence the Parity-OBDD representation size gives way for the development of heuristic algorithms for their minimization. The results of these analyses as well as the efficiency of the data structure are also supported by experiments. Finally, the algorithmic concept of Parity-OBDDs is extended to Mod-p-Decision Diagrams (Mod-p-DDs) for the representation of functions that are defined over an arbitrary finite domain.