otvl

Orthogonal ternary vector lists (OTVL)

Contents

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 $x_i$, the element 0 represents $(1-x_i)$ and the don't care operator - represents multiplication with the neutral element 1. Hence, a TVL

x1x2x3
110
1-1
000

can be represented as a multilinear function

$$x_1x_2(1-x_3) + x_1x_3 + (1-x_1)(1-x_2)(1-x_3).$$

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