The polynomial-time reduction from sat to csat, as described in section 10.3.3 (p. 452), needs to introduce new variables. the reason is that the obvious manipulation of a boolean expression into an equivalent cnf expression could exponentiate the size of the expression, and therefore could not be polynomial time. suppose we apply this construction to the expression (u+(vw))+x, with the parse implied by the parentheses. suppose also that when we introduce new variables, we use y1, after constructing the corresponding cnf expression, identify one of its clauses from the list below.
note: logical or is represented by +, logical and by juxtaposition, and logical not by -.