Computational complexity is concerned with the complexity of solving
 problems and computing functions and not with the complexity of verifying
 circuit designs.
 The importance of formal circuit verification is evident.
 Therefore, a framework of a complexity theory for formal circuit
 verification with binary decision diagrams ...
                	
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We survey some upper and lower bounds established recently on
 the sizes of randomized branching programs computing explicit
 boolean functions. In particular, we display boolean
 functions on which randomized read-once ordered branching
 programs are exponentially more powerful than deterministic
 or nondeterministic read-$k$-times branching programs for ...
                	
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