Generating functionology
Statistical properties of simple types
Mathematical Structures in Computer Science
Combinatorics, Probability and Computing
On asymptotic divergency in equivalential logics
Mathematical Structures in 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
Intuitionistic vs. classical tautologies, quantitative comparison
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
The fraction of large random trees representing a given Boolean function in implicational logic
Random Structures & Algorithms
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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In this paper we study the asymptotic behavior of the fraction of true formulas against all formulas over k propositional variables with equivalence as the only connective in the language. We consider two ways of measuring the asymptotic behavior. In the first case we investigate the size of the tautology fraction of length n against the number of all formulas of length n. The second case is very similar and we investigate the size of the tautology fraction of length at most n against the number of all formulas of length at most n. In both cases we are interested in finding the limit (which is often called ''density'' and ''cumulative density'', respectively) of each fraction when n-~. It was already proved that the asymptotic density for k=1 exists for all binary connectives except equivalence. In this paper we prove that for every k there are exactly two accumulation points for the language based on equivalence: 0, 1/2^k^-^1 for asymptotic density and 1/2^k^-^1(4k+1), 4k/2^k^-^1(4k+1) for cumulative asymptotic density.