Algorithms and Data Structures in VLSI Design OBDD - Foundations and Applications

One of the main problems in chip design is the huge number of possible combinations of individual chip elements, leading to a combinatorial explosion as chips become more complex. New key results in theoretical computer science and in the design of data structures and efficient algorithms, can be applied fruitfully here. The application of ordered binary decision diagrams (OBDDs) has led to dramatic performance improvements in many computer-aided design projects. This textbook provides an introduction to the foundations of this interdisciplinary research area with an emphasis on applications in computer-aided circuit design and formal verification.

1. Introduction.- 2. Basics.- 2.1 Propositions and Predicates.- 2.2 Sets, Relations, and Functions.- 2.3 Graphs.- 2.4 Algorithms and Data Structures.- 2.5 Complexity of Algorithms.- 2.6 Hashing.- 2.7 Finite Automata and Finite State Machines.- 2.8 References.- I. Data Structures for Switching Functions.- 3. Boolean Functions.- 4. Classical Representations.- 5. Requirements on Data Structures in Formal Circuit Verification.- II. OBDDs: An Efficient Data Structure.- 6. OBDDs — Ordered Binary Decision Diagrams.- 7. Efficient Implementation of OBDDs.- 8. Influence of the Variable Order on the Complexity of OBDDs.- 9. Optimizing the Variable Order.- III. Applications and Extensions.- 10. Analysis of Sequential Systems.- 11. Symbolic Model Checking.- 12. Variants and Extensions of OBDDs.- 13. Transformation Techniques for Optimization.