The monotone circuit complexity of Boolean functions
Combinatorica
The complexity of Boolean functions
The complexity of Boolean functions
Limiting negations in constant depth circuits
SIAM Journal on Computing
Characterizing non-deterministic circuit size
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of 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
Limiting Negations in Formulas
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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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, in particular, proved that @?log"2(n+1)@? NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and determine the inversion complexity of every Boolean function. In particular, we prove that one NOT gate is sufficient to compute any Boolean function in non-deterministic circuits if we can use an arbitrary number of guess inputs.