An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Using amplification to compute majority with small majority gates
Computational Complexity
Systems of functional equations
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Some typical properties of large AND/OR Boolean formulas
Random Structures & Algorithms
Coloring rules for finite trees, and probabilities of monadic second order sentences
Random Structures & Algorithms
Statistical properties of simple types
Mathematical Structures in Computer Science
Combinatorics, Probability and Computing
The Boolean functions computed by random Boolean formulas or how to grow the right function
Random Structures & Algorithms
On asymptotic divergency in equivalential logics
Mathematical Structures in Computer Science
Amplification of probabilistic boolean formulas
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Complexity and Limiting Ratio of Boolean Functions over Implication
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Analytic Combinatorics
Quantitative Comparison of Intuitionistic and Classical Logics - Full Propositional System
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Asymptotic Density for Equivalence
Electronic Notes in Theoretical Computer Science (ENTCS)
Classical and intuitionistic logic are asymptotically identical
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We consider the logical system of Boolean expressions built on the single connector of implication and on positive literals. Assuming all expressions of a given size to be equally likely, we prove that we can define a probability distribution on the set of Boolean functions expressible in this system. Then we show how to approximate the probability of a function f when the number of variables grows to infinity, and that this asymptotic probability has a simple expression in terms of the complexity of f. We also prove that most expressions computing any given function in this system are “simple”, in a sense that we make precise. The probability of all read-once functions of a given complexity is also evaluated in this model. At last, using the same techniques, the relation between the probability of a function and its complexity is also obtained when random expressions are drawn according to a critical branching process. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 © 2012 Wiley Periodicals, Inc. (A preliminary version of this work appeared in MFCS'08. Supported by FWF (Austrian Science Foundation), National Research Area S9600 (S9604), ÖAD (F03/2010); A.N.R. projects SADA, BOOLE, P.H.C. Amadeus project Probabilities and tree representations for Boolean functions.)