In this paper, we discussed several problems in the design of hardware algorithms and logic design automation. The theory of complexty of logic circuits and parallel computation will form the foundation of design of hardware algorithms which will become more important for larger VLSI systems. Especially, the relation between the complexities of software and hardware is very important for practical system design, because systems are combination of software and hardware. Design automation is one of the most highlighted fields in computer science. There are still many hard problems to solve in developing much efficient design automation system. Researches on high-level hardware design languages, automatic logic design from descriptions of three languages and design verification techniques for large systems have been increasing. Several techniques developed in the software engineering will be applied to these area.