
doi: 10.46298/dmtcs.3475
We examine how we can define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees. Analytic tools give us a systematic way to prove the existence of probability distributions, the main challenge being the actual computation of the distributions. We finally consider the relations between the probability of a Boolean function and its complexity.
[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], [info.info-hc] computer science [cs]/human-computer interaction [cs.hc], [info.info-sc] computer science [cs]/symbolic computation [cs.sc], [info.info-lo] computer science [cs]/logic in computer science [cs.lo], probability of tautologies, boolean function, probability distribution for boolean functions, Boolean function, QA1-939, [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], complexity, Mathematics, probability distribution for Boolean functions
[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], [info.info-hc] computer science [cs]/human-computer interaction [cs.hc], [info.info-sc] computer science [cs]/symbolic computation [cs.sc], [info.info-lo] computer science [cs]/logic in computer science [cs.lo], probability of tautologies, boolean function, probability distribution for boolean functions, Boolean function, QA1-939, [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], complexity, Mathematics, probability distribution for Boolean functions
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