Rephrasing: A Decision-Wait receives two bits of data in a Double-Rail code via the a and b inputs and converts them to a four-wire One-Hot code via the c outputs. Phrased yet differently: It awaits two binary decisions and reports the combination.
Specification in Verdect:
define JOIN2X2( a0?, a1?, b0?, b1?, c00!, c01!, c10!, c11! ) =
pref *[ (a0? || b0?); c00!
| (a0? || b1?); c01!
| (a1? || b0?); c10!
| (a1? || b1?); c11!
]
end
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The Decision-Wait is very symmetric, having 8 automorphisms.
The roles of subscripts 0 and 1 can be interchanged,
independently on both a and on b,
and also the roles of a and b can be interchanged,
provided that the c outputs are permuted accordingly:
DW(a_0, a_1, b_0, b_1;
c_00, c_01, c_10, c_11) =
DW(a_1, a_0, b_0, b_1;
c_10, c_11, c_00, c_01) =
DW(a_0, a_1, b_1, b_0;
c_01, c_00, c_11, c_10) =
DW(a_1, a_0, b_1, b_0;
c_11, c_10, c_01, c_00) =
DW(b_0, b_1, a_0, a_1;
c_00, c_10, c_01, c_11) =
DW(b_1, b_0, a_0, a_1;
c_01, c_11, c_00, c_10) =
DW(b_0, b_1, a_1, a_0;
c_10, c_00, c_11, c_01) =
DW(b_1, b_0, a_1, a_0;
c_11, c_01, c_10, c_00)
The Decision-Wait satisfies Rules Y' and Z^out, but not Z^in (choice between a inputs, and also between b inputs).
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It can be further generalized to an n-dimensional v-decision-wait with #v=n>0, which awaits n choices, choice i being among v.i inputs, and reports the combination as a choice between (PROD i: 0 <= i < n: v.i) outputs. A Decision-Wait is a 2-dimensional (2,2)-Decision-Wait.
In [Molnar74, Part 1, Volume III, p. 13], the Decision-Wait and its generalizations are referred to as D Element.
In terms of [Ebergen89, p. 88], the Decision-Wait and its two-dimensional generalizations are CAL components. In [Ebergen89, pp. 95-99], decompositions of CAL components in terms of ... are presented.
Conjecture: A Decision-Wait cannot be implemented with only Forks, Joins, Merges, Latches (or even Sequencers), and I-Wires.
