boofun.core.representations.ltf

Linear Threshold Function (LTF) representation for Boolean functions.

A Linear Threshold Function is defined by: f(x) = sign(w₁x₁ + w₂x₂ + … + wₙxₙ - θ)

where w = (w₁, w₂, …, wₙ) are the weights and θ is the threshold.

Functions

create_majority_ltf(n_vars)	Create LTF for majority function.
create_threshold_ltf(n_vars, k)	Create LTF for k-threshold function.
is_ltf(truth_table, n_vars)	Check if a Boolean function can be represented as an LTF.

Classes

LTFParameters(weights, threshold, n_vars)	Parameters for a Linear Threshold Function.
LTFRepresentation()	Linear Threshold Function representation for Boolean functions.

class boofun.core.representations.ltf.LTFParameters(weights: ndarray, threshold: float, n_vars: int)

Parameters for a Linear Threshold Function.

weights

Array of weights for each variable

Type:

numpy.ndarray

threshold

Threshold value

Type:

float

n_vars

Number of variables

Type:

int

weights: ndarray

threshold: float

n_vars: int

evaluate(x: List[int] | ndarray) → bool

Evaluate LTF at given input.

Parameters:

x – Binary input vector

Returns:

Boolean output

to_dict() → Dict[str, Any]

Export LTF parameters to dictionary.

classmethod from_dict(data: Dict[str, Any]) → LTFParameters

Create LTF parameters from dictionary.

__init__(weights: ndarray, threshold: float, n_vars: int) → None

class boofun.core.representations.ltf.LTFRepresentation

Linear Threshold Function representation for Boolean functions.

evaluate(inputs: ndarray, data: LTFParameters, space: Space, n_vars: int) → bool | ndarray

Evaluate LTF representation.

Parameters:

• inputs – Input values (integer indices or binary vectors)

• data – LTF parameters

• space – Evaluation space

• n_vars – Number of variables

Returns:

Boolean result(s)

dump(data: LTFParameters, space=None, **kwargs) → Dict[str, Any]

Export LTF representation.

convert_from(source_repr: BooleanFunctionRepresentation, source_data: Any, space: Space, n_vars: int, **kwargs) → LTFParameters

Convert from another representation to LTF.

Uses linear programming to find weights and threshold. Note: Not all Boolean functions can be represented as LTFs.

convert_to(target_repr: BooleanFunctionRepresentation, source_data: Any, space: Space, n_vars: int, **kwargs) → ndarray

Convert LTF to another representation.

create_empty(n_vars: int, **kwargs) → LTFParameters

Create empty LTF (constant False).

is_complete(data: LTFParameters) → bool

Check if LTF is complete (has valid parameters).

time_complexity_rank(n_vars: int) → Dict[str, int]

Return time complexity for LTF operations.

get_storage_requirements(n_vars: int) → Dict[str, int]

Return storage requirements for LTF representation.

boofun.core.representations.ltf.is_ltf(truth_table: List[bool], n_vars: int) → bool

Check if a Boolean function can be represented as an LTF.

Parameters:

• truth_table – Boolean truth table

• n_vars – Number of variables

Returns:

True if function is linearly separable

boofun.core.representations.ltf.create_majority_ltf(n_vars: int) → LTFParameters

Create LTF for majority function.

Parameters:

n_vars – Number of variables (must be odd)

Returns:

LTF parameters for majority function

boofun.core.representations.ltf.create_threshold_ltf(n_vars: int, k: int) → LTFParameters

Create LTF for k-threshold function.

Parameters:

• n_vars – Number of variables

• k – Threshold (output 1 if at least k variables are 1)

Returns:

LTF parameters for threshold function