The monotone circuit complexity of Boolean functions
Combinatorica
The complexity of Boolean functions
The complexity of Boolean functions
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Limiting negations in constant depth circuits
SIAM Journal on Computing
Poceedings of the London Mathematical Society symposium on Boolean function complexity
The Shrinkage Exponent of de Morgan Formulas is 2
SIAM Journal on Computing
On the Complexity of Negation-Limited Boolean Networks
SIAM Journal on Computing
On the Inversion Complexity of a System of Functions
Journal of the ACM (JACM)
On the negation-limited circuit complexity of merging
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Hauptvortrag: The complexity of negation-limited networks - A brief survey
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On the minimum number of negations leading to super-polynomial savings
Information Processing Letters
Negation-Limited Inverters of Linear Size
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Note: Limiting negations in non-deterministic circuits
Theoretical Computer Science
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Negation-limited circuits have been studied as a circuit model between general circuits and monotone circuits. In this paper, we consider limiting negations in formulas. The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ***log2 (n + 1) *** NOT gates are sufficient to compute any Boolean function on n variables. We determine the inversion complexity of every Boolean function in formulas, i.e., the minimum number of NOT gates (NOT operators) in a Boolean formula computing (representing) a Boolean function, and particularly prove that ***n /2 *** NOT gates are sufficient to compute any Boolean function on n variables. Moreover we show that if there is a polynomial-size formula computing a Boolean function f , then there is a polynomial-size formula computing f with at most ***n /2 *** NOT gates. We consider also the inversion complexity in formulas of negation normal form and prove that the inversion complexity is at most polynomials of n for every Boolean function on n variables.