## 7 Citations

### Asymptotic Properties of Logics

- Mathematics
- 2003

This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies…

### The fraction of large random trees representing a given Boolean function in implicational logic

- Computer Science, MathematicsRandom Struct. Algorithms
- 2012

The relation between the probability of a function and its complexity is obtained when random expressions are drawn according to a critical branching process and it is proved that most expressions computing any given function in this system are “simple”.

### Complexity and Limiting Ratio of Boolean Functions over Implication

- Computer Science, MathematicsMFCS
- 2008

It is shown 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.

### Analysis of Algorithms DMTCS proc . AD , 2005 , 139 – 146 And / or tree probabilities of Boolean functions

- Computer Science, Mathematics
- 2005

Two probability distributions on Boolean functions defined in terms of their representations by a d/or trees (or formulas) are considered, with special attention being paid to the constant function True and read-once functions in a fixed number of variables.

### And/or tree probabilities of Boolean functions

- Computer Science, Mathematics
- 2005

Two probability distributions on Boolean functions defined in terms of their representations by $\texttt{and/or}$ trees (or formulas) are considered, with special attention being paid to the constant function $\textit{True}$ and read-once functions in a fixed number of variables.

### Random Boolean expressions

- Computer Science, Mathematics
- 2005

This work examines how to 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 and considers the relations between the probability of a Boolean function and its complexity.

## References

SHOWING 1-5 OF 5 REFERENCES

### Statistics of Intuitionistic versus Classical Logics

- PhilosophyStud Logica
- 2004

This paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part of classical prepositional calculus and may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.

### Advanced Combinatorics: The Art of Finite and Infinite Expansions

- Mathematics
- 1974

I. Vocabulary of Combinatorial Analysis.- 1.1. Subsets of a Set Operations.- 1.2. Product Sets.- 1.3. Maps.- 1.4. Arrangements, Permutations.- 1.5. Combinations (without repetitions) or Blocks.- 1.6.…

### Orthogonal Polynomials

- Mathematics
- 2005

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

### Statistical properties of simple types

- MathematicsMathematical Structures in Computer Science
- 2000

From the lower and upper bounds presented, it is deduced that at least 1/3 of classical tautologies are intuitionistic, or the density or asymptotic probability of provable intuitionistic propositional formulas in the set of all formulas.

### A remark on Stirling formula , Ammer

- . Math . Monthly
- 1955