Waych, Edward

Edward Veitch grew up in the small town of Dumont , New Jersey . In 1942 he entered Harvard University . In the middle of the first year he was called up for active military service, where he studied physics and engineering under a special program, after which he was involved in the Manhattan project in Los Alamos, New Mexico, where he served as an electronic technician. After the war, Veich returned to Harvard and in 1946 received a bachelor's degree in physics, and then a master's degree in physics and applied physics, in 1948 and 1949, respectively. He studied with Howard Aiken , the creator of Mark I , the first American programmable computer .

Since 1949, Veich worked at Burroughs Corporation , in the development team of one of the very first electronic computer systems, both commercial and military, and received a number of patents ^{[4] [5] [6] [7]} . These projects included the E101 computer, and the network processing system for information received from SAGE radars . At this time, he published an article on the method of optimizing digital circuits ^[2] , which is now known as the method of Veitch diagrams. Veich led research and development of computer systems at the RCA computer department, and later at Pennsylvania Research Associates (Philadelphia) ^{[8] [9] [10] [11] [12] [13] [14] [15]} . While working at RCA's Missile and Surface Radar Division, he developed computer systems for the Navy's Aegis Missile Defense System .

He was married to Natalie (Ford) and left behind 2 children: daughter Laurel and son Andrew.

Veitch's Comments

On the development of his diagrams and their interpretation, Veich wrote the following.

• The problem is to depict a Boolean function of n variables so that the human eye can easily see how to simplify it.
• The function of four variables has sixteen input combinations and, accordingly, the diagram contains sixteen squares, which must be filled using the truth table of the corresponding function.
• The main difference between the versions of Veitch and Carnot is that the Veitch diagrams represent the data in the binary sequence used in the truth table, whereas in the Carnot charts the third and fourth rows and the third and fourth columns are interchanged.
• The computer community has chosen Carnot's approach. Veitch made this decision, despite the fact that at the beginning of 1952, before his presentation, he wanted to choose the same approach, but decided not to. A few years later, a description of Carnot maps appeared in textbooks, and in some of them they were called Veitch diagrams.

In 1999, Veitch discovered a Wikipedia article on Carnot maps. He read it and, after re-reading his work in 1952, he realized that the method of minimization was not described in it. Now he believes that readers of his article believed that he was doing minimization by looking at the designations of columns and rows, and those who used Carnot cards minimized groups by the rules, and then used labels only to identify groups.

Veitch also believes that the changes he made in his charts immediately before their presentation made it difficult to apply his rules for finding minimal groups.

Original Veich Charts

It was known that functions could be represented as points in the corners of an n-dimensional cube. Two adjacent corners, for example two upper right corners, can be defined as upper right corners, and four corners on the front face of the cube can be defined as front corners. For four, five, or six variables, the problem becomes even more complex.

How to draw a multidimensional cube in a flat diagram so that you can easily see these relationships?

• For three dimensions, Veitch drew a set of 2x2 squares for the top of the cube, and a second for the bottom of the cube with a small gap between the two sets of squares. In the upper 2x2 set, the minimized group was a horizontal or vertical pair of cells or all four cells. The connection between the upper and lower sets was represented as a one-to-one relationship between each square of the upper set and the corresponding cell of the lower set. A similar rule applies to the case of four variables, which is sometimes depicted as a cube, inside another cube in which all the corresponding angles are connected.
• The Veitch diagrams for four variables will then be depicted as four sets of 2x2 large squares with a small space between each pair of sets. Thus, the horizontal pair in the upper left set can be combined with the corresponding pair in the lower left set or upper right set or, possibly, with all four sets, making up a group of take cells.
• For five or six variables, the same rule applies. The diagram for five variables consists of two diagrams for four variables located next to each other with a large gap between them. The coincidence between two diagrams for four variables is found for cells that coincide if one card is superimposed on another.

At the last minute before the presentation, Veich removed the gap between the 2x2 cell groups. This was a bad decision, because it complicated the understanding of the general structure of the function, as well as the application of minimization rules. Later, solving Sudoku puzzles, Veitch realized that having gaps or thick lines between groups of squares can be very useful, especially if you have poor eyesight like Veitch did in old age. ^[sixteen]

• Carnot Map

Veitch, Edward W. A proof regarding infinite nets of logic elements without feedback. FOCS 1965, 1965, pp. 162–167.