According to Moore's law, Integrated Chips (IC) doubles its capacity every 18 months. This causes an exponential increase of the available area, and hence,the complexity of modern digital designs. This consistent enormous gross challenges different research areas in Electronic Design Automation (EDA). Thus, various EDA applications such as equivalence checking, model checking, Automatic Test Pattern Generation (ATPG), functional Bi-decomposition, and technology mapping need to keep pace with these challenges. In this thesis, we are concerned with improving the quality and performance of different EDA algorithms particularly in area of hardware verification and synthesis. First, we introduce algorithms to manipulate Reduced Ordered Binary Decision Diagrams (ROBDD) on multi-core machines. In order to perform multiple BDD operations concurrently, our algorithm uses a breadth-first search (BFS). As ROBDD algorithms are memory-intensive, maintaining locality of data is an important issue. Therefore, we propose the usage of Hopscotch hashing technique for both Unique Table and BFS Queues to improve the construction time of ROBDD on the parallel platform. Hopscotch hashing technique not only improves the locality of the manipulating data, but also provides a way to cache recently performed BDD operation. Consequently, The time and space usage can be traded off. Secondly, we used static implications to enhance the performance of SAT-based Bounded Model Checking (BMC) problem. we propose a parallel deduction engine to efficiently utilize low-cost off-shelf multi-core processors to compute the implications. With this engine, we can significantly reduce the computational processing time in analyzing the deduced implications. Secondly, we formulate the clause filter problem as an elegant set-covering problem. Thirdly, we propose a novel greedy algorithm based on the Johnson's algorithm to find the optimal set of clauses that would accelerate BMC solution. Thirdly, we proposed a novel synthesis paradigm to achieve timing-closure called Timing-Aware CUt Enumeration (TACUE). In TACUE, optimization is conducted through three aspects: First, we propose a new divide-and-conquer strategy that generates multiple sub-cuts on the critical parts of the circuit. Secondly, cut enumeration have been applied in two cutting strategies. In the topology-aware cutting strategy, we preserve the general topology of the circuit by applying TACUE in only self-contained cuts. Meanwhile, the topology-masking cutting strategy investigates circuit cuts beyond their current topology. Thirdly, we proposed an efficient parallel synthesis framework to reduce computation time for synthesizing TACUE sub-cuts. We conducted experiments on large and difficult industrial benchmarks. Finally, we proposed the first scalable SAT-based approaches for Observability Dont Care (ODC) clock gating. Moreover we intelligently choose those inductive invariants candidates such that their validation will benefit the purpose in clock-gating-based low-power design. / Ph. D.