Coders, decoders and recognizers

On the left, the coder is shown in the moment of its activation. On the right, it is shown just after the generation of the activation train propagating along the output line (the pulse sequence corresponds to the bit sequence 10101001 in reverse order). The coding procedure exploits four basic properties common to both JVN and EVN transition rules: 1) The bifurcation of an activation train at a confluent-state. 2) The relative delays of activation trains propagating along transmission lines of different length. 3) The one-step delay caused by the transit of an activation train across a confluent-state. 4) The logical OR of activation trains converging to a transmission line.

Sometime, however, the Author, found it often preferable to exploit various informal tricks to create coders of irregular shape minimum size. The automaton-file CODER_COLLECTION.EVN and the fragment-file CODER_COLLECTION.EFR contain a wide repertoire of such informal coders with their characteristic activation trains indicated aside.

The decoders are another important class of automaton organs. Their role is detecting whether a given activation train contains a certain bit sequence as a subsequence. This process is often sufficient to discriminate different activation trains, for instance when working with multiplexers. To perform the filtering function, the decoder exploits the logical AND property of two activation trains converging to a confluent state working as a coincidence device. The figure here below shows a decoder as designed by von Neumann.

At input, the activation train carrying the bit sequence 10101001 enters the coder. At output, a single pulse is emitted. Were there only a single 1 missing from the bit-sequence, the decoder would not emit the output pulse. The cell assembly reported above evidences the decoding procedure. The activation train propagating along the input line bifurcates at 4 confluent states equally spaced along the input-line continuation. Note that there are as many bifurcations as there are ones in the bit sequence. The upward transmission lines stemming from these bifurcations have different lengths, in order to cause suitable delays, and converge to the output line through confluent states working as logical ANDs. Thus, an activation pulse reaches the output line only when two pulses target simultaneously all logical ANDs. The time delays are chosen so that: (1) the pulse transmitted by the first upward-line reaches the first logical AND (second confluent state in the output line) in coincidence with the pulse coming from the second upward-line. (2) The pulse transmitted by this confluent state reaches the next logical AND (third confluent state in the output line) in coincidence with that coming from the third upward-line, etc. Note that the relative delays between consecutive upward-lines (from left to right) are exactly 2, 2, 3, which correspond one-to-one to the numbers of zeros in the sequence 10101001, i.e., 2-1, 2-1, 3-1.

This property can be generalized to decode activation trains of any sort. As with coders, there are alternative ways to implement decoders. The automaton-file DECODERS.EVN and the fragment-file DECODER.EFR contain a few examples of coder-decoder pairs with their respective characteristic activation trains indicated underneath the connection lines.

A decoder simply checks whether an activation train contains a given bit-sequence as a subsequence, but not whether it carries a precise bit sequence. The organs capable of performing the latter operation are called recognizers. Since a bit sequence has more "ones" than any one of its proper subsequences, to build a recognizer it suffices that the pulse released by the decoder is cancelled if the activation train contains more pulses than expected. Indeed, the recognizers described in von Neumann & Burks' book, are nothing else but decoders provided with a secondary organ that do just this. The cancellation of the pulse at output is usually performed by exploiting a property of the special transmission states (red arrows): a pulse delivered by a red arrow annihilates any ordinary transmission state (blue arrow) that it points to, no matter whether quiescent or not. Actually, the cancellation is caused by the annihilation of a right blue-arrow in the output line before the arrival of the pulse released by the decoder. Thus, when the pulse meets this vacuum state, instead of passing, a sensitized-state sequence restores the missing right arrow.

The secondary organ (underneath the input-line level) is not a pulse counter but a coder that generates a repetitive sequence of pulses (of input-depending length) if the input train has the expected number of pulses, otherwise a sequence with at least one gap if the number of pulses. The device must then work so that the pulse at output disappears unless the activation train generated by the coder has at least one gap. The propagation of this secondary train is timed in such a way that at a gap reaches the confluent state near the red arrow in coincidence with the pulse emitted by the decoder. Since this confluent state behaves as a logical AND, the red arrow releases a pulse only if the activation train has a gap.

The automaton-file RECOGNIZERS.EVN and the fragment-file RECOGNIZERS.EFR contain several examples of such recognizers with their characteristic bit-sequences indicated aside. These organs are used in the universal constructors and self-reproducing automata described in the EVN-automaton gallery to control the actions of the C-arm in correspondence with particular activation train working as specific signals.