Unit Description

Class Diagram

classDiagram
    comp_wptt_vertex_canonicity ..|> computation
    comp_wptt_vertex_canonicity_config_t ..|> notation_wptt
    comp_wptt_vertex_canonicity_config_t ..|> comp_config_t
    comp_wptt_vertex_canonicity *-- comp_wptt_vertex_canonicity_config_t
    comp_wptt_vertex_canonicity_result_t ..|> notation_wptt
    comp_wptt_vertex_canonicity_result_t ..|> comp_result_t
    comp_wptt_vertex_canonicity *-- comp_wptt_vertex_canonicity_result_t
    comp_wptt_vertex_canonicity_result_t *-- comp_wptt_vertex_canonicity_positivity_e

    class computation {
    <<External Interface>>
    }

    class comp_wptt_vertex_canonicity {
    <<External>>
    }

    class notation_wptt{
    <<External>>
    }

    class comp_wptt_vertex_canonicity_config_t {
    + notation_node_wptt *vertex
    + notation_node_wptt *parent
    + comp_wptt_vertex_canonicity_positivity_e positivity
    }

    class comp_config_t {
    <<External Interface>>
    }

    class comp_wptt_vertex_canonicity_result_t {
    + bool is_canonical
    }

    class comp_wptt_vertex_canonicity_positivity_e {
    <<Enumeration>>
     uninit,
     positive,
     negative,
    }

    class comp_result_t {
    <<External Interface>>
    }

Language

C

Implements

Computation Interface

Uses

Notation Weighted Planar Tangle Tree

Libraries

None

Functionality

Public Structures

Configuration Structure

The configuration structure contains the data needed for computing the canonicity of a vertex of an input arborescent tangle.

This includes:

A pointer to the tree containing the vertex. This is used only for output to the write interface.
A pointer to the vertex to examine.
A pointer to the parent of the vertex being examined.
The positivity condition to check.

Result Structure

The result structure contains the enumerated value of the neutrality of the input tree.

Public Functions

Configuration Function

The configuration function sets the local configuration variable of the computation.

This process is described in the following state machines:

stateDiagram-v2
  state "Initialize local configuration" as Sc

    [*] --> Sc
    Sc --> [*]

Compute Function

The compute function carries out the arborescent tangle vertex canonicity computation. The function may contain sub-machines that can be broken out into functions in the implementation. The walk the tree function should be implemented with a stack-based iterative approach.

This process is described in the following state machines:

stateDiagram-v2
    state "Set result to false" as false
    state "Set result to true" as true
    state is_stick <<choice>>
    state is_weight <<choice>>
    state is_positive <<choice>>
    state is_root <<choice>>
    [*] --> is_weight
    is_weight --> false: else
    is_weight --> is_root: Vertex satisfies the weight condition
    is_root --> false: else
    is_root --> is_stick: Vertex is the root
    is_stick --> false: else
    is_stick --> is_positive: Vertex satisfies the sitck condition
    is_positive --> false: else
    is_positive --> true: Vertex satisfies the positivity condition
    true --> [*]
    false --> [*]

Result Function

When this function is invoked, the result of the vertex canonicity computation process is reported.

Validation

Configuration Function

Positive Tests

Valid Configuration

A valid configuration for the computation is passed to the function.

Inputs:

A valid configuration.

Expected Output:

A positive response.

Negative Tests

Null Configuration

A null configuration for the computation is passed to the function.

Inputs:

A null configuration.

Expected Output:

A negative response.

Null Configuration Parameters

A configuration with various null parameters is passed to the function.

Inputs:

A configuration with null tree.

Expected Output:

A negative response.

Compute Function

Positive Tests

A valid configuration with null write interface

A valid configuration is set for the component with null write. The computation is executed and returns successfully.

Inputs:

A valid configuration is set.

Expected Output:

A positive response.

Identified vertex is canonical

A valid configuration with write function is set for the component. The indentified vertex is canonical. The computation is executed and returns successfully.

Inputs:

A valid configuration is set.
The identified vertex is canonical:
- Is the root
- Is away from root
The positivity is set to:
- positive
- negative

**Expected Output:**

- A positive response.
- True written to buffer

Identified vertex violates the alternating stick condition

A valid configuration with write function is set for the component. The indentified vertex fails to be canonical by violating the alternating portion of the stick condition. The computation is executed and returns successfully.

Inputs:

A valid configuration is set.
The identified vertex is not canonical by violating:
- vertex is \(v_0\) and \(w_0<0\) with \(w_1<0\)
- vertex is \(v_0\) and \(w_0>0\) with \(w_1>0\)
- vertex is \(v_i\) with \(i\neq 0\) and \(w_{i}>0\) with \(w_{i+1}>0\)
- vertex is \(v_i\) with \(i\neq 0\) and \(w_{i}<0\) with \(w_{i+1}<0\)

Expected Output:

A positive response.
False written to buffer.

Identified vertex is not canonical