Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
M.S. Paterson , Warwick Univ., Coventry, UK
U. Zwick , Warwick Univ., Coventry, UK
It is shown that a random restriction leaving only a fraction in of the input variables unassigned reduces the expected de Morgan formula size of the induced function by a factor of O( in /sup 1.63/). This is an improvement over previous results. The new exponent yields an increased lower bound of approximately n/sup 2.63/ for the de Morgan formula size of a function in P defined by A.E. Andreev (1987). This is the largest lower bound known, even for functions in NP.
NP, de Morgan formulae, random restriction, induced function, lower bound
U. Zwick and M. Paterson, "Shrinkage of de Morgan formulae under restriction,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 324-333.