# otvl

Orthogonal ternary vector lists (OTVL)

## Contents

- Syntax
- Description
- Input arguments
- Output arguments
- Example create OTVL
- References
- See Also

## Syntax

`obj = otvl(otvlArray)`

## Description

Use `obj = otvl(otvlArray)` to create an otvl object containing an OTVL.

Ternary vector lists arise from the field of Boolean algebra and find frequent usage in the Boolean Calculus [1]. Since Boolean functions are a subclass of multinlinear functions, OTVLs can serve as the basis for an efficient representation of a subclass of multilinear functions, see also [2]. OTVLs consist of a combination of three value types, that are logical true (1), logical false (0) and a "don't care operator" (-).

OTVLs can be represented as multilinear functions by multiplication of the elements in a row and addition of the rows. The element 1 in the OTVL represents the variable , the element 0 represents and the don't care operator - represents multiplication with the neutral element 1. Hence, a TVL

x1 | x2 | x3
--- | --- | ---
1 | 1 | 0
1 | - | 1
0 | 0 | 0

can be represented as a multilinear function

## Input arguments

`otvlArray` 3D array marking the positions of don't care operators, logical true and false in the OTVL

## Output arguments

`obj` otvl object

## Example create OTVL

An OTVL is stored as a threedimensional structure. The first dimension indicates the rows of the OTVL, the second dimension the columns. The third dimension stores the information about the value type. myotvl(:,:,1) contains the position of don't care values, while myotvl(:,:,2) contains the Boolean values.

    % Create OTVL structure
    myTvlStruct1= false(3,3,2);
    myTvlStruct1(:,:,1) = [0 0 0; 0 1 0; 0 0 0]; %position of dont cares
    myTvlStruct1(:,:,2) = [1 1 0; 1 0 1; 0 0 0]; %Boolean values (position of logical true)

An otvl-object is then created by using the constructor method of the class otvl.

    % Create  OTVL
    myOTvl1 = otvl(myTvlStruct1);

## References

[1] B. Steinbach, C. Posthof "Logic Functions and Equations - Fundamentals and Applications using the XBOOLE-Monitor", 3rd Ed. Cham, Weitzerland: Springer, 2023

[2] M. Engels, G. Lichtenberg, and S. Knorn. "An approach to structured multilinear modeling with relaxed Boolean output functions", in 22nd IFAC World Congress, Yokohama, Japan, 2023, pp.7920-7925

## See Also

otvlTens