In the first half of this thesis, a novel approach for k-induction bounded model checking using signal domain constraints and property partitioning for proving unreachability of branches in Verilog RTL code is presented. To do this, it approach uses program slicing with respect to the variables of the property under test to generate small-sized SMT formulas that describe the change of variable values between consecutive cycles. Variable substitution is then used on these variables to generate the formula for the subsequent cycles without traversing the abstract syntax tree of the entire design. To reduce the approximation on the induction step, an addition of signal domain constraints is proposed. Moreover, we present the technique for splitting up the property in question to get a better model of the system. The later half of the thesis is concerned with presenting a technique for doing sequential vector compaction on test set generated during simulation based ATPG. Starting with a compaction framework for storing metadata and about the test vectors during generation, this work presented to methods for findind the solution of this compaction problem. The first of these two methods generate the optimum solution by converting the problem appropriate for an optimization solver. The latter method utilizes a heuristics based approach for solving the same problem which generates a comparable but sub-optimal solution while having magnitudes better time and computational efficiency.