With the advances in VLSI and System-On-Chip (SOC) technology, the complexity of hardware systems has increased manifold. Today, 70% of the design cost is spent in verifying these intricate systems. The two most widely used formal methods for design verification are Equivalence Checking and Model Checking. Equivalence Checking requires that the implementation circuit should be exactly equivalent to the specification circuit (golden model). In other words, for each possible input pattern, the implementation circuit should yield the same outputs as the specification circuit. Model checking, on the other hand, checks to see if the design holds certain properties, which in turn are indispensable for the proper functionality of the design. Complexities in both Equivalence Checking and Model Checking are exponential to the circuit size. In this thesis, we firstly propose a novel technique to improve SAT-based Combinational Equivalence Checking (CEC) and Bounded Model Checking (BMC). The idea is to perform a low-cost preprocessing that will statically induce global signal relationships into the original CNF formula of the circuit under verification and hence reduce the complexity of the SAT instance. This efficient and effective preprocessing quickly builds up the implication graph for the circuit under verification, yielding a large set of logic implications composed of direct, indirect and extended backward implications. These two-node implications (spanning time-frame boundaries) are converted into two-literal clauses, and added to the original CNF database. The added clauses constrain the search space of the SAT-solver engine, and provide correlation among the different variables, which enhances the Boolean Constraint Propagation (BCP). Experimental results on large and difficult ISCAS'85, ISCAS'89 (full scan) and ITC'99 (full scan) CEC instances and ISCAS'89 BMC instances show that our approach is independent of the state-of-the-art SAT-solver used, and that the added clauses help to achieve more than an order of magnitude speedup over the conventional approach. Also, comparison with Hyper-Resolution [Bacchus 03] suggests that our technique is much more powerful, yielding non-trivial clauses that significantly simplify the SAT instance complexity. Secondly, we propose a novel global learning technique that helps to identify highly non-trivial relationships among signals in the circuit netlist, thereby boosting the power of the existing implication engine. We call this new class of implications as 'extended forward implications', and show its effectiveness through additional untestable faults they help to identify. Thirdly, we propose a suite of lemmas and theorems to formalize global learning. We show through implementation that these theorems help to significantly simplify a generic CNF formula (from Formal Verification, Artificial Intelligence etc.) by identifying the necessary assignments, equivalent signals, complementary signals and other non-trivial implication relationships among its variables. We further illustrate through experimental results that the CNF formula simplification obtained using our tool outshines the simplification obtained using other preprocessors. / Master of Science