# Random Formula Generators

• Published in 2021
In the collection
In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces.

## Other information

key
RandomFormulaGenerators
type
article
2024-03-11
date_published
2021-09-05

### BibTeX entry

@article{RandomFormulaGenerators,
key = {RandomFormulaGenerators},
type = {article},
title = {Random Formula Generators},
author = {Ariel J. Roffe and Joaquin S. Toranzo Calderon},
abstract = {In this article, we provide three generators of propositional formulae for
arbitrary languages, which uniformly sample three different formulae spaces.
They take the same three parameters as input, namely, a desired depth, a set of
atomics and a set of logical constants (with specified arities). The first
generator returns formulae of exactly the given depth, using all or some of the
propositional letters. The second does the same but samples up-to the given
depth. The third generator outputs formulae with exactly the desired depth and
all the atomics in the set. To make the generators uniform (i.e. to make them
return every formula in their space with the same probability), we will prove
various cardinality results about those spaces.},
comment = {},
}