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Boolean satisfiability (SAT) solvers are used heavily in hardware and software verification tools for checking satisfiability of Boolean formulas. Most state-of-the-art SAT solvers are based on the Davis-Putnam-Logemann-Loveland (DPLL) algorithm and require the input formula to be in conjunctive normal form (CNF). We present a new SAT solver that operates on the negation normal form (NNF) of the given Boolean formulas/circuits. The NNF of a formula is usually more succinct than the CNF of the formula in terms of the number of variables. Our algorithm applies the DPLL algorithm to the graph-based representations of NNF formulas. We adapt the idea of the two-watched-literal scheme from CNF SAT solvers in order to efficiently carry out Boolean Constraint Propagation (BCP), a key task in the DPLL algorithm. We evaluate the new solver on a large collection of Boolean circuit benchmarks obtained from formal verification problems. The new solver outperforms the top solvers of the SAT 2007 competition and SAT-Race 2008 in terms of run time on a large majority of the benchmarks.