Rule:Semaphore

@RULE Semaphore

by _zM, 2022

Period 1 circuitry rule with builtin crossovers and memory cells.

0: dead 1: Wire 2: Signal head 3: Signal tail 4: Signal body 5: OFF semaphore 6: ON semaphore

Neighbors only count if they meet one of the following criteria: Diagonally adjacent cells: a) with two dead neighbors b) with two live neighbors Orthogonally adjacent cells: c) with two dead neighbors d) with one live neighbor that itself has a dead neighbor e) with two live neighbors, each with a dead neighbor

Wires can be either ON or OFF and store the state they were in in the previous generation; they can therefore take on four CA states. Semaphores can also be both ON or OFF; they do not store history.

If a wire is connected to at least two other wires, it acts as wire or a splitter. If all touching

wires agree in their current state, then the wire takes on that state; otherwise it takes on the inverse of its previous state.

If a wire is connected to only one other wire, its behavior depends on the number of connected

semaphores. If it is connected to none or one, the wire takes on the current state of its only wire neighbor. Otherwise it acts as a gate, taking as inputs its semaphore neighbors XORed with its previous state.

A two-input gate is an AND gate.
A three-input gate acts as a complex latch. This is the only place in the entire rule wihere input

configuration matters; the input opposite the output wire (B) is treated separately from the two other inputs (A and C).

The output also depends on the gate's current state, represented as Q:

B   A+C   Q'

---

0    0    Q
0    1    1
0    2    0
1    0    0
1    1    Q
1    2   !Q

If semaphores are connected only to wire cells, their state toggles whenever the XOR of the current

and past staes of all neighbors is odd; if they are connected to other semaphores their behavior is undefined.

@TABLE

n_states: 7 neighborhood: Moore symmetries: rotate4reflect

1. All states

var a0 = {0, 1, 2, 3, 4, 5, 6} var a1 = a0 var a2 = a0 var a3 = a0 var a4 = a0 var a5 = a0 var a6 = a0 var a7 = a0 var a8 = a0

1. Live states

var w0 = {1, 2, 3, 4, 5, 6} var w1 = w0 var w2 = w0 var w3 = w0 var w4 = w0 var w5 = w0 var w6 = w0 var w7 = w0 var w8 = w0

1. Wire states

var v0 = {1, 2, 3, 4} var v1 = v0 var v2 = v0 var v3 = v0 var v4 = v0 var v5 = v0 var v6 = v0 var v7 = v0 var v8 = v0

1. Active wire

var l0 = {2, 4} var l1 = l0 var l2 = l0 var l3 = l0 var l4 = l0 var l5 = l0 var l6 = l0 var l7 = l0 var l8 = l0

1. Inactive wire

var d0 = {1, 3} var d1 = d0 var d2 = d0 var d3 = d0 var d4 = d0 var d5 = d0 var d6 = d0 var d7 = d0 var d8 = d0

1. History XORs to 1

var p0 = {2, 3} var p1 = p0 var p2 = p0 var p3 = p0 var p4 = p0 var p5 = p0 var p6 = p0 var p7 = p0 var p8 = p0

1. History XORs to 0

var n0 = {1, 4} var n1 = n0 var n2 = n0 var n3 = n0 var n4 = n0 var n5 = n0 var n6 = n0 var n7 = n0 var n8 = n0

1. Semaphore states

var c0 = {5, 6} var c1 = c0 var c2 = c0 var c3 = c0 var c4 = c0 var c5 = c0 var c6 = c0 var c7 = c0 var c8 = c0

1. 0 neighbors: keep state

1. 0
2. I 0 0 0 0 0 0 0 0 O

1. 1 neighbor:
2. wire: copy neighbor
3. SEM: XOR

1. 1c
2. I A w A A? 0 0 0 A? O

d0, 0,d2, 0, 0, 0, 0, 0, 0, 1 d0, 0,l2, 0, 0, 0, 0, 0, 0, 2 l0, 0,d2, 0, 0, 0, 0, 0, 0, 3 l0, 0,l2, 0, 0, 0, 0, 0, 0, 4 c0, 0,n2, 0, 0, 0, 0, 0, 0,c0

5, 0,p2, 0, 0, 0, 0, 0, 0, 6
6, 0,p2, 0, 0, 0, 0, 0, 0, 5

d0,w1,d2,w3,a4, 0, 0, 0,a8, 1 d0,w1,l2,w3,a4, 0, 0, 0,a8, 2 l0,w1,d2,w3,a4, 0, 0, 0,a8, 3 l0,w1,l2,w3,a4, 0, 0, 0,a8, 4 c0,w1,n2,w3,a4, 0, 0, 0,a8,c0

5,w1,p2,w3,a4, 0, 0, 0,a8, 6
6,w1,p2,w3,a4, 0, 0, 0,a8, 5

1. 1e
2. I w  ? 0 0 0 0 0  ? O

d0,d1,a2, 0, 0, 0, 0, 0,a8, 1 d0,l1,a2, 0, 0, 0, 0, 0,a8, 2 l0,d1,a2, 0, 0, 0, 0, 0,a8, 3 l0,l1,a2, 0, 0, 0, 0, 0,a8, 4 c0,n1,a2, 0, 0, 0, 0, 0,a8,c0

5,p1,a2, 0, 0, 0, 0, 0,a8, 6
6,p1,a2, 0, 0, 0, 0, 0,a8, 5

1. 2 neighbors:
2. wire: copy non-SEM neighbor, else copy both if they agree,
3. else copy whichever one prev gen disagrees with
4. SEM: XOR

1. 2c
2. I 0 A? A w A w A A? O

v0, 0, 0, 0,c4, 0,v6, 0, 0,v6 d0, 0, 0, 0,d4, 0,d6, 0, 0, 1 d0, 0, 0, 0,l4, 0,l6, 0, 0, 2 l0, 0, 0, 0,d4, 0,d6, 0, 0, 3 l0, 0, 0, 0,l4, 0,l6, 0, 0, 4

1, 0, 0, 0,v4, 0,v6, 0, 0, 2
2, 0, 0, 0,v4, 0,v6, 0, 0, 4
3, 0, 0, 0,v4, 0,v6, 0, 0, 1
4, 0, 0, 0,v4, 0,v6, 0, 0, 3

c0, 0, 0, 0,p4, 0,p6, 0, 0,c0 c0, 0, 0, 0,n4, 0,n6, 0, 0,c0

5, 0, 0, 0,v4, 0,v6, 0, 0, 6
6, 0, 0, 0,v4, 0,v6, 0, 0, 5

v0, 0,a2,w3,c4,w5,v6,w7,a8,v6 d0, 0,a2,w3,d4,w5,d6,w7,a8, 1 d0, 0,a2,w3,l4,w5,l6,w7,a8, 2 l0, 0,a2,w3,d4,w5,d6,w7,a8, 3 l0, 0,a2,w3,l4,w5,l6,w7,a8, 4

1, 0,a2,w3,v4,w5,v6,w7,a8, 2
2, 0,a2,w3,v4,w5,v6,w7,a8, 4
3, 0,a2,w3,v4,w5,v6,w7,a8, 1
4, 0,a2,w3,v4,w5,v6,w7,a8, 3

c0, 0,a2,w3,p4,w5,p6,w7,a8,c0 c0, 0,a2,w3,n4,w5,n6,w7,a8,c0

5, 0,a2,w3,v4,w5,v6,w7,a8, 6
6, 0,a2,w3,v4,w5,v6,w7,a8, 5

1. 2e
2. I 0  ? w 0 w  ? 0 0 O

v0, 0,a2,c3, 0,v5,a6, 0, 0,v5 d0, 0,a2,d3, 0,d5,a6, 0, 0, 1 d0, 0,a2,l3, 0,l5,a6, 0, 0, 2 l0, 0,a2,d3, 0,d5,a6, 0, 0, 3 l0, 0,a2,l3, 0,l5,a6, 0, 0, 4

1, 0,a2,v3, 0,v5,a6, 0, 0, 2
2, 0,a2,v3, 0,v5,a6, 0, 0, 4
3, 0,a2,v3, 0,v5,a6, 0, 0, 1
4, 0,a2,v3, 0,v5,a6, 0, 0, 3

c0, 0,a2,p3, 0,p5,a6, 0, 0,c0 c0, 0,a2,n3, 0,n5,a6, 0, 0,c0

5, 0,a2,v3, 0,v5,a6, 0, 0, 6
6, 0,a2,v3, 0,v5,a6, 0, 0, 5

1. 2k
2. I 0  ? w A !AB w !AB<-? O

v0, 0,a2,c3,a4, 0,v6, 0, 0,v6 v0, 0,a2,v3,a4, 0,c6, 0, 0,v3 d0, 0,a2,d3,a4, 0,d6, 0, 0, 1 d0, 0,a2,l3,a4, 0,l6, 0, 0, 2 l0, 0,a2,d3,a4, 0,d6, 0, 0, 3 l0, 0,a2,l3,a4, 0,l6, 0, 0, 4

1, 0,a2,v3,a4, 0,v6, 0, 0, 2
2, 0,a2,v3,a4, 0,v6, 0, 0, 4
3, 0,a2,v3,a4, 0,v6, 0, 0, 1
4, 0,a2,v3,a4, 0,v6, 0, 0, 3

c0, 0,a2,p3,a4, 0,p6, 0, 0,c0 c0, 0,a2,n3,a4, 0,n6, 0, 0,c0

5, 0,a2,v3,a4, 0,v6, 0, 0, 6
6, 0,a2,v3,a4, 0,v6, 0, 0, 5

v0, 0,a2,c3, 0,w5,v6,w7,a8,v6 v0, 0,a2,v3, 0,w5,c6,w7,a8,v3 d0, 0,a2,d3, 0,w5,d6,w7,a8, 1 d0, 0,a2,l3, 0,w5,l6,w7,a8, 2 l0, 0,a2,d3, 0,w5,d6,w7,a8, 3 l0, 0,a2,l3, 0,w5,l6,w7,a8, 4

1, 0,a2,v3, 0,w5,v6,w7,a8, 2
2, 0,a2,v3, 0,w5,v6,w7,a8, 4
3, 0,a2,v3, 0,w5,v6,w7,a8, 1
4, 0,a2,v3, 0,w5,v6,w7,a8, 3

c0, 0,a2,p3, 0,w5,p6,w7,a8,c0 c0, 0,a2,n3, 0,w5,n6,w7,a8,c0

5, 0,a2,v3, 0,w5,v6,w7,a8, 6
6, 0,a2,v3, 0,w5,v6,w7,a8, 5

1. 2i
2. I 0  ? w  ? 0  ? w  ? O

v0, 0,a2,c3,a4, 0,a6,v7,a8,v7 d0, 0,a2,d3,a4, 0,a6,d7,a8, 1 d0, 0,a2,l3,a4, 0,a6,l7,a8, 2 l0, 0,a2,d3,a4, 0,a6,d7,a8, 3 l0, 0,a2,l3,a4, 0,a6,l7,a8, 4

1, 0,a2,v3,a4, 0,a6,v7,a8, 2
2, 0,a2,v3,a4, 0,a6,v7,a8, 4
3, 0,a2,v3,a4, 0,a6,v7,a8, 1
4, 0,a2,v3,a4, 0,a6,v7,a8, 3

c0, 0,a2,p3,a4, 0,a6,p7,a8,c0 c0, 0,a2,n3,a4, 0,a6,n7,a8,c0

5, 0,a2,v3,a4, 0,a6,v7,a8, 6
6, 0,a2,v3,a4, 0,a6,v7,a8, 5

1. 2n
2. I A w A AXB B w B AxB O

v0, 0,c2, 0, 0, 0,v6, 0, 0,v6 d0, 0,d2, 0, 0, 0,d6, 0, 0, 1 d0, 0,l2, 0, 0, 0,l6, 0, 0, 2 l0, 0,d2, 0, 0, 0,d6, 0, 0, 3 l0, 0,l2, 0, 0, 0,l6, 0, 0, 4

1, 0,v2, 0, 0, 0,v6, 0, 0, 2
2, 0,v2, 0, 0, 0,v6, 0, 0, 4
3, 0,v2, 0, 0, 0,v6, 0, 0, 1
4, 0,v2, 0, 0, 0,v6, 0, 0, 3

c0, 0,p2, 0, 0, 0,p6, 0, 0,c0 c0, 0,n2, 0, 0, 0,n6, 0, 0,c0

5, 0,v2, 0, 0, 0,v6, 0, 0, 6
6, 0,v2, 0, 0, 0,v6, 0, 0, 5

v0,w1,c2,w3,a4, 0,v6, 0,a8,v6 v0,w1,v2,w3,a4, 0,c6, 0,a8,v2 d0,w1,d2,w3,a4, 0,d6, 0,a8, 1 d0,w1,l2,w3,a4, 0,l6, 0,a8, 2 l0,w1,d2,w3,a4, 0,d6, 0,a8, 3 l0,w1,l2,w3,a4, 0,l6, 0,a8, 4

1,w1,v2,w3,a4, 0,v6, 0,a8, 2
2,w1,v2,w3,a4, 0,v6, 0,a8, 4
3,w1,v2,w3,a4, 0,v6, 0,a8, 1
4,w1,v2,w3,a4, 0,v6, 0,a8, 3

c0,w1,p2,w3,a4, 0,p6, 0,a8,c0 c0,w1,n2,w3,a4, 0,n6, 0,a8,c0

5,w1,v2,w3,a4, 0,v6, 0,a8, 6
6,w1,v2,w3,a4, 0,v6, 0,a8, 5

v0,w1,c2,w3, 0,w5,v6,w7, 0,v6 d0,w1,d2,w3, 0,w5,d6,w7, 0, 1 d0,w1,l2,w3, 0,w5,l6,w7, 0, 2 l0,w1,d2,w3, 0,w5,d6,w7, 0, 3 l0,w1,l2,w3, 0,w5,l6,w7, 0, 4

1,w1,v2,w3, 0,w5,v6,w7, 0, 2
2,w1,v2,w3, 0,w5,v6,w7, 0, 4
3,w1,v2,w3, 0,w5,v6,w7, 0, 1
4,w1,v2,w3, 0,w5,v6,w7, 0, 3

c0,w1,p2,w3, 0,w5,p6,w7, 0,c0 c0,w1,n2,w3, 0,w5,n6,w7, 0,c0

5,w1,v2,w3, 0,w5,v6,w7, 0, 6
6,w1,v2,w3, 0,w5,v6,w7, 0, 5

1. 3 neighbors:
2. wire:
3. no sem -> splitter
4. 1 sem -> splitter
5. 2 sem -> AND (sems XOR out) gate
6. 3 sem -> unused
7. sem: XOR

1. 3c
2. I A w A W A w A 0 O

1. 0 sems

d0, 0,d2, 0,d4, 0,d6, 0, 0, 1 d0, 0,l2, 0,l4, 0,l6, 0, 0, 2 l0, 0,d2, 0,d4, 0,d6, 0, 0, 3 l0, 0,l2, 0,l4, 0,l6, 0, 0, 4

1, 0,v2, 0,v4, 0,v6, 0, 0, 2
2, 0,v2, 0,v4, 0,v6, 0, 0, 4
3, 0,v2, 0,v4, 0,v6, 0, 0, 1
4, 0,v2, 0,v4, 0,v6, 0, 0, 3

c0, 0,p2, 0,n4, 0,p6, 0, 0,c0 c0, 0,p2, 0,p4, 0,n6, 0, 0,c0 c0, 0,n2, 0,n4, 0,n6, 0, 0,c0

5, 0,v2, 0,v4, 0,v6, 0, 0, 6
6, 0,v2, 0,v4, 0,v6, 0, 0, 5

d0,w1,d2,w3,d4,w5,d6,w7, 0, 1 d0,w1,l2,w3,l4,w5,l6,w7, 0, 2 l0,w1,d2,w3,d4,w5,d6,w7, 0, 3 l0,w1,l2,w3,l4,w5,l6,w7, 0, 4

1,w1,v2,w3,v4,w5,v6,w7, 0, 2
2,w1,v2,w3,v4,w5,v6,w7, 0, 4
3,w1,v2,w3,v4,w5,v6,w7, 0, 1
4,w1,v2,w3,v4,w5,v6,w7, 0, 3

c0,w1,p2,w3,n4,w5,p6,w7, 0,c0 c0,w1,p2,w3,p4,w5,n6,w7, 0,c0 c0,w1,n2,w3,n4,w5,n6,w7, 0,c0

5,w1,v2,w3,v4,w5,v6,w7, 0, 6
6,w1,v2,w3,v4,w5,v6,w7, 0, 5

1. 1 sem

1, 0,d2, 0,d4, 0,c6, 0, 0, 1
2, 0,d2, 0,d4, 0,c6, 0, 0, 3
3, 0,l2, 0,l4, 0,c6, 0, 0, 2
4, 0,l2, 0,l4, 0,c6, 0, 0, 4
1, 0,v2, 0,v4, 0,c6, 0, 0, 2
2, 0,v2, 0,v4, 0,c6, 0, 0, 4
3, 0,v2, 0,v4, 0,c6, 0, 0, 1
4, 0,v2, 0,v4, 0,c6, 0, 0, 3

1, 0,d2, 0,c4, 0,d6, 0, 0, 1
2, 0,d2, 0,c4, 0,d6, 0, 0, 3
3, 0,l2, 0,c4, 0,l6, 0, 0, 2
4, 0,l2, 0,c4, 0,l6, 0, 0, 4
1, 0,v2, 0,c4, 0,v6, 0, 0, 2
2, 0,v2, 0,c4, 0,v6, 0, 0, 4
3, 0,v2, 0,c4, 0,v6, 0, 0, 1
4, 0,v2, 0,c4, 0,v6, 0, 0, 3

1,w1,d2,w3,d4,w5,c6,w7, 0, 1
2,w1,d2,w3,d4,w5,c6,w7, 0, 3
3,w1,l2,w3,l4,w5,c6,w7, 0, 2
4,w1,l2,w3,l4,w5,c6,w7, 0, 4
1,w1,v2,w3,v4,w5,c6,w7, 0, 2
2,w1,v2,w3,v4,w5,c6,w7, 0, 4
3,w1,v2,w3,v4,w5,c6,w7, 0, 1
4,w1,v2,w3,v4,w5,c6,w7, 0, 3

1,w1,d2,w3,c4,w5,d6,w7, 0, 1
2,w1,d2,w3,c4,w5,d6,w7, 0, 3
3,w1,l2,w3,c4,w5,l6,w7, 0, 2
4,w1,l2,w3,c4,w5,l6,w7, 0, 4
1,w1,v2,w3,c4,w5,v6,w7, 0, 2
2,w1,v2,w3,c4,w5,v6,w7, 0, 4
3,w1,v2,w3,c4,w5,v6,w7, 0, 1
4,w1,v2,w3,c4,w5,v6,w7, 0, 3

1. 2 sems

1, 0, 6, 0, 6, 0,v6, 0, 0, 2
2, 0, 6, 0, 6, 0,v6, 0, 0, 4
3, 0, 5, 0, 5, 0,v6, 0, 0, 2
4, 0, 5, 0, 5, 0,v6, 0, 0, 4

d0, 0,c2, 0,c4, 0,v6, 0, 0, 1 l0, 0,c2, 0,c4, 0,v6, 0, 0, 3

1, 0, 6, 0,v4, 0, 6, 0, 0, 2
2, 0, 6, 0,v4, 0, 6, 0, 0, 4
3, 0, 5, 0,v4, 0, 5, 0, 0, 2
4, 0, 5, 0,v4, 0, 5, 0, 0, 4

d0, 0,c2, 0,v4, 0,c6, 0, 0, 1 l0, 0,c2, 0,v4, 0,c6, 0, 0, 3

1,w1, 6,w3, 6,w5,v6,w7, 0, 2
2,w1, 6,w3, 6,w5,v6,w7, 0, 4
3,w1, 5,w3, 5,w5,v6,w7, 0, 2
4,w1, 5,w3, 5,w5,v6,w7, 0, 4

d0,w1,c2,w3,c4,w5,v6,w7, 0, 1 l0,w1,c2,w3,c4,w5,v6,w7, 0, 3

1,w1, 6,w3,v4,w5, 6,w7, 0, 2
2,w1, 6,w3,v4,w5, 6,w7, 0, 4
3,w1, 5,w3,v4,w5, 5,w7, 0, 2
4,w1, 5,w3,v4,w5, 5,w7, 0, 4

d0,w1,c2,w3,v4,w5,c6,w7, 0, 1 l0,w1,c2,w3,v4,w5,c6,w7, 0, 3

1. 3 sems

1. 3e
2. I 0  ? w 0 W 0 w  ? O

1. 0 sems

d0, 0,a2,d3, 0,d5, 0,d7,a8, 1 d0, 0,a2,l3, 0,l5, 0,l7,a8, 2 l0, 0,a2,d3, 0,d5, 0,d7,a8, 3 l0, 0,a2,l3, 0,l5, 0,l7,a8, 4

1, 0,a2,v3, 0,v5, 0,v7,a8, 2
2, 0,a2,v3, 0,v5, 0,v7,a8, 4
3, 0,a2,v3, 0,v5, 0,v7,a8, 1
4, 0,a2,v3, 0,v5, 0,v7,a8, 3

c0, 0,a2,p3, 0,n5, 0,p7,a8,c0 c0, 0,a2,p3, 0,p5, 0,n7,a8,c0 c0, 0,a2,n3, 0,n5, 0,n7,a8,c0

5, 0,a2,v3, 0,v5, 0,v7,a8, 6
6, 0,a2,v3, 0,v5, 0,v7,a8, 5

1. 1 sem

1, 0,a2,d3, 0,d5, 0,c7,a8, 1
2, 0,a2,d3, 0,d5, 0,c7,a8, 3
3, 0,a2,l3, 0,l5, 0,c7,a8, 2
4, 0,a2,l3, 0,l5, 0,c7,a8, 4
1, 0,a2,v3, 0,v5, 0,c7,a8, 2
2, 0,a2,v3, 0,v5, 0,c7,a8, 4
3, 0,a2,v3, 0,v5, 0,c7,a8, 1
4, 0,a2,v3, 0,v5, 0,c7,a8, 3

1, 0,a2,d3, 0,c5, 0,d7,a8, 1
2, 0,a2,d3, 0,c5, 0,d7,a8, 3
3, 0,a2,l3, 0,c5, 0,l7,a8, 2
4, 0,a2,l3, 0,c5, 0,l7,a8, 4
1, 0,a2,v3, 0,c5, 0,v7,a8, 2
2, 0,a2,v3, 0,c5, 0,v7,a8, 4
3, 0,a2,v3, 0,c5, 0,v7,a8, 1
4, 0,a2,v3, 0,c5, 0,v7,a8, 3

1. 2 sems

1, 0,a2, 6, 0, 6, 0,v7,a8, 2
2, 0,a2, 6, 0, 6, 0,v7,a8, 4
3, 0,a2, 5, 0, 5, 0,v7,a8, 2
4, 0,a2, 5, 0, 5, 0,v7,a8, 4

d0, 0,a2,c3, 0,c5, 0,v7,a8, 1 l0, 0,a2,c3, 0,c5, 0,v7,a8, 3

1, 0,a2, 6, 0,v5, 0, 6,a8, 2
2, 0,a2, 6, 0,v5, 0, 6,a8, 4
3, 0,a2, 5, 0,v5, 0, 5,a8, 2
4, 0,a2, 5, 0,v5, 0, 5,a8, 4

d0, 0,a2,c3, 0,v5, 0,c7,a8, 1 l0, 0,a2,c3, 0,v5, 0,c7,a8, 3

1. 3 sems

1. 3k
2. I w !A? A w A !A? w 0 O

1. 0 sems

d0,d1,a2, 0,d4, 0,a6,d7, 0, 1 d0,l1,a2, 0,l4, 0,a6,l7, 0, 2 l0,d1,a2, 0,d4, 0,a6,d7, 0, 3 l0,l1,a2, 0,l4, 0,a6,l7, 0, 4

1,v1,a2, 0,v4, 0,a6,v7, 0, 2
2,v1,a2, 0,v4, 0,a6,v7, 0, 4
3,v1,a2, 0,v4, 0,a6,v7, 0, 1
4,v1,a2, 0,v4, 0,a6,v7, 0, 3

c0,p1,a2, 0,n4, 0,a6,p7, 0,c0 c0,p1,a2, 0,p4, 0,a6,n7, 0,c0 c0,n1,a2, 0,n4, 0,a6,n7, 0,c0

5,v1,a2, 0,v4, 0,a6,v7, 0, 6
6,v1,a2, 0,v4, 0,a6,v7, 0, 5

d0,d1, 0,w3,d4,w5, 0,d7, 0, 1 d0,l1, 0,w3,l4,w5, 0,l7, 0, 2 l0,d1, 0,w3,d4,w5, 0,d7, 0, 3 l0,l1, 0,w3,l4,w5, 0,l7, 0, 4

1,v1, 0,w3,v4,w5, 0,v7, 0, 2
2,v1, 0,w3,v4,w5, 0,v7, 0, 4
3,v1, 0,w3,v4,w5, 0,v7, 0, 1
4,v1, 0,w3,v4,w5, 0,v7, 0, 3

c0,p1, 0,w3,n4,w5, 0,p7, 0,c0 c0,p1, 0,w3,p4,w5, 0,n7, 0,c0 c0,n1, 0,w3,n4,w5, 0,n7, 0,c0

5,v1, 0,w3,v4,w5, 0,v7, 0, 6
6,v1, 0,w3,v4,w5, 0,v7, 0, 5

1. 1 sem

1,d1,a2, 0,d4, 0,a6,c7, 0, 1
2,d1,a2, 0,d4, 0,a6,c7, 0, 3
3,l1,a2, 0,l4, 0,a6,c7, 0, 2
4,l1,a2, 0,l4, 0,a6,c7, 0, 4
1,v1,a2, 0,v4, 0,a6,c7, 0, 2
2,v1,a2, 0,v4, 0,a6,c7, 0, 4
3,v1,a2, 0,v4, 0,a6,c7, 0, 1
4,v1,a2, 0,v4, 0,a6,c7, 0, 3

1,d1,a2, 0,c6, 0,a6,d7, 0, 1
2,d1,a2, 0,c6, 0,a6,d7, 0, 3
3,l1,a2, 0,c6, 0,a6,l7, 0, 2
4,l1,a2, 0,c6, 0,a6,l7, 0, 4
1,v1,a2, 0,c4, 0,a6,v7, 0, 2
2,v1,a2, 0,c4, 0,a6,v7, 0, 4
3,v1,a2, 0,c4, 0,a6,v7, 0, 1
4,v1,a2, 0,c4, 0,a6,v7, 0, 3

1,d1, 0,w3,d4,w5, 0,c7, 0, 1
2,d1, 0,w3,d4,w5, 0,c7, 0, 3
3,l1, 0,w3,l4,w5, 0,c7, 0, 2
4,l1, 0,w3,l4,w5, 0,c7, 0, 4
1,v1, 0,w3,v4,w5, 0,c7, 0, 2
2,v1, 0,w3,v4,w5, 0,c7, 0, 4
3,v1, 0,w3,v4,w5, 0,c7, 0, 1
4,v1, 0,w3,v4,w5, 0,c7, 0, 3

1,d1, 0,w3,c6,w5, 0,d7, 0, 1
2,d1, 0,w3,c6,w5, 0,d7, 0, 3
3,l1, 0,w3,c6,w5, 0,l7, 0, 2
4,l1, 0,w3,c6,w5, 0,l7, 0, 4
1,v1, 0,w3,c4,w5, 0,v7, 0, 2
2,v1, 0,w3,c4,w5, 0,v7, 0, 4
3,v1, 0,w3,c4,w5, 0,v7, 0, 1
4,v1, 0,w3,c4,w5, 0,v7, 0, 3

1. 2 sems

1, 6,a2, 0, 6, 0,a6,v7, 0, 2
2, 6,a2, 0, 6, 0,a6,v7, 0, 4
3, 5,a2, 0, 5, 0,a6,v7, 0, 2
4, 5,a2, 0, 5, 0,a6,v7, 0, 4

d0,c1,a2, 0,c4, 0,a6,v7, 0, 1 l0,c1,a2, 0,c4, 0,a6,v7, 0, 3

1, 6,a2, 0,v4, 0,a6, 6, 0, 2
2, 6,a2, 0,v4, 0,a6, 6, 0, 4
3, 5,a2, 0,v4, 0,a6, 5, 0, 2
4, 5,a2, 0,v4, 0,a6, 5, 0, 4

d0,c1,a2, 0,v4, 0,a6,c7, 0, 1 l0,c1,a2, 0,v4, 0,a6,c7, 0, 3

1, 6, 0,w3, 6,w5, 0,v7, 0, 2
2, 6, 0,w3, 6,w5, 0,v7, 0, 4
3, 5, 0,w3, 5,w5, 0,v7, 0, 2
4, 5, 0,w3, 5,w5, 0,v7, 0, 4

d0,c1, 0,w3,c4,w5, 0,v7, 0, 1 l0,c1, 0,w3,c4,w5, 0,v7, 0, 3

1, 6, 0,w3,v4,w5, 0, 6, 0, 2
2, 6, 0,w3,v4,w5, 0, 6, 0, 4
3, 5, 0,w3,v4,w5, 0, 5, 0, 2
4, 5, 0,w3,v4,w5, 0, 5, 0, 4

d0,c1, 0,w3,v4,w5, 0,c7, 0, 1 l0,c1, 0,w3,v4,w5, 0,c7, 0, 3

1. 3y
2. I A w A w A !A? W !A? O

1. 0 sems

d0, 0,d2, 0,d4, 0,a6,d7,a8, 1 d0, 0,l2, 0,l4, 0,a6,l7,a8, 2 l0, 0,d2, 0,d4, 0,a6,d7,a8, 3 l0, 0,l2, 0,l4, 0,a6,l7,a8, 4

1, 0,v2, 0,v4, 0,a6,v7,a8, 2
2, 0,v2, 0,v4, 0,a6,v7,a8, 4
3, 0,v2, 0,v4, 0,a6,v7,a8, 1
4, 0,v2, 0,v4, 0,a6,v7,a8, 3

c0, 0,p2, 0,n4, 0,a6,p7,a8,c0 c0, 0,p2, 0,p4, 0,a6,n7,a8,c0 c0, 0,n2, 0,n4, 0,a6,n7,a8,c0

5, 0,v2, 0,v4, 0,a6,v7,a8, 6
6, 0,v2, 0,v4, 0,a6,v7,a8, 5

d0,w1,d2,w3,d4,w5, 0,d7, 0, 1 d0,w1,l2,w3,l4,w5, 0,l7, 0, 2 l0,w1,d2,w3,d4,w5, 0,d7, 0, 3 l0,w1,l2,w3,l4,w5, 0,l7, 0, 4

1,w1,v2,w3,v4,w5, 0,v7, 0, 2
2,w1,v2,w3,v4,w5, 0,v7, 0, 4
3,w1,v2,w3,v4,w5, 0,v7, 0, 1
4,w1,v2,w3,v4,w5, 0,v7, 0, 3

c0,w1,p2,w3,n4,w5, 0,p7, 0,c0 c0,w1,p2,w3,p4,w5, 0,n7, 0,c0 c0,w1,n2,w3,n4,w5, 0,n7, 0,c0

5,w1,v2,w3,v4,w5, 0,v7, 0, 6
6,w1,v2,w3,v4,w5, 0,v7, 0, 5

1. 1 sem

1, 0,d2, 0,d4, 0,a6,c7,a8, 1
2, 0,d2, 0,d4, 0,a6,c7,a8, 3
3, 0,l2, 0,l4, 0,a6,c7,a8, 2
4, 0,l2, 0,l4, 0,a6,c7,a8, 4
1, 0,v2, 0,v4, 0,a6,c7,a8, 2
2, 0,v2, 0,v4, 0,a6,c7,a8, 4
3, 0,v2, 0,v4, 0,a6,c7,a8, 1
4, 0,v2, 0,v4, 0,a6,c7,a8, 3

1, 0,d2, 0,c4, 0,a6,d7,a8, 1
2, 0,d2, 0,c4, 0,a6,d7,a8, 3
3, 0,l2, 0,c4, 0,a6,l7,a8, 2
4, 0,l2, 0,c4, 0,a6,l7,a8, 4
1, 0,v2, 0,c4, 0,a6,v7,a8, 2
2, 0,v2, 0,c4, 0,a6,v7,a8, 4
3, 0,v2, 0,c4, 0,a6,v7,a8, 1
4, 0,v2, 0,c4, 0,a6,v7,a8, 3

1,w1,d2,w3,d4,w5, 0,c7, 0, 1
2,w1,d2,w3,d4,w5, 0,c7, 0, 3
3,w1,l2,w3,l4,w5, 0,c7, 0, 2
4,w1,l2,w3,l4,w5, 0,c7, 0, 4
1,w1,v2,w3,v4,w5, 0,c7, 0, 2
2,w1,v2,w3,v4,w5, 0,c7, 0, 4
3,w1,v2,w3,v4,w5, 0,c7, 0, 1
4,w1,v2,w3,v4,w5, 0,c7, 0, 3

1,w1,d2,w3,c4,w5, 0,d7, 0, 1
2,w1,d2,w3,c4,w5, 0,d7, 0, 3
3,w1,l2,w3,c4,w5, 0,l7, 0, 2
4,w1,l2,w3,c4,w5, 0,l7, 0, 4
1,w1,v2,w3,c4,w5, 0,v7, 0, 2
2,w1,v2,w3,c4,w5, 0,v7, 0, 4
3,w1,v2,w3,c4,w5, 0,v7, 0, 1
4,w1,v2,w3,c4,w5, 0,v7, 0, 3

1. 2 sems

1, 0, 6, 0, 6, 0,a6,v7,a8, 2
2, 0, 6, 0, 6, 0,a6,v7,a8, 4
3, 0, 5, 0, 5, 0,a6,v7,a8, 2
4, 0, 5, 0, 5, 0,a6,v7,a8, 4

d0, 0,c2, 0,c4, 0,a6,v7,a8, 1 l0, 0,c2, 0,c4, 0,a6,v7,a8, 3

1, 0, 6, 0,v4, 0,a6, 6,a8, 2
2, 0, 6, 0,v4, 0,a6, 6,a8, 4
3, 0, 5, 0,v4, 0,a6, 5,a8, 2
4, 0, 5, 0,v4, 0,a6, 5,a8, 4

d0, 0,c2, 0,v4, 0,a6,c7,a8, 1 l0, 0,c2, 0,v4, 0,a6,c7,a8, 3

1,w1, 6,w3, 6,w5, 0,v7, 0, 2
2,w1, 6,w3, 6,w5, 0,v7, 0, 4
3,w1, 5,w3, 5,w5, 0,v7, 0, 2
4,w1, 5,w3, 5,w5, 0,v7, 0, 4

d0,w1,c2,w3,c4,w5, 0,v7, 0, 1 l0,w1,c2,w3,c4,w5, 0,v7, 0, 3

1,w1, 6,w3,v4,w5, 0, 6, 0, 2
2,w1, 6,w3,v4,w5, 0, 6, 0, 4
3,w1, 5,w3,v4,w5, 0, 5, 0, 2
4,w1, 5,w3,v4,w5, 0, 5, 0, 4

d0,w1,c2,w3,v4,w5, 0,c7, 0, 1 l0,w1,c2,w3,v4,w5, 0,c7, 0, 3

1. 4 neighbors:
2. wire:
3. no sem -> splitter
4. 1 sem -> splitter
5. 2 sems -> splitter
6. 3 sems -> E latch + T latch + ...
7. 4 sems -> unused
8. sem: XOR

1. 3 sems:
2. B A+C Q'
3. 0 0 Q
4. 0 1 1
5. 0 2 0
6. 1 0 0
7. 1 1 Q
8. 1 2 !Q

1. E latch: Hold one of the outer inputs low
2. T latch: Hold one outer and the middle input high

1. 4c
2. I A w A w A w A w O

1. 0 sems

d0, 0,d2, 0,d4, 0,d6, 0,d8, 1 d0, 0,l2, 0,l4, 0,l6, 0,l8, 2 l0, 0,d2, 0,d4, 0,d6, 0,d8, 3 l0, 0,l2, 0,l4, 0,l6, 0,l8, 4

1, 0,v2, 0,v4, 0,v6, 0,v8, 2
2, 0,v2, 0,v4, 0,v6, 0,v8, 4
3, 0,v2, 0,v4, 0,v6, 0,v8, 1
4, 0,v2, 0,v4, 0,v6, 0,v8, 3

c0, 0,p2, 0,p4, 0,p6, 0,p8,c0 c0, 0,p2, 0,n4, 0,p6, 0,n8,c0 c0, 0,p2, 0,p4, 0,n6, 0,n8,c0 c0, 0,n2, 0,n4, 0,n6, 0,n8,c0

5, 0,v2, 0,v4, 0,v6, 0,v8, 6
6, 0,v2, 0,v4, 0,v6, 0,v8, 5

d0,w1,d2,w3,d4,w5,d6,w7,d8, 1 d0,w1,l2,w3,l4,w5,l6,w7,l8, 2 l0,w1,d2,w3,d4,w5,d6,w7,d8, 3 l0,w1,l2,w3,l4,w5,l6,w7,l8, 4

1,w1,v2,w3,v4,w5,v6,w7,v8, 2
2,w1,v2,w3,v4,w5,v6,w7,v8, 4
3,w1,v2,w3,v4,w5,v6,w7,v8, 1
4,w1,v2,w3,v4,w5,v6,w7,v8, 3

c0,w1,p2,w3,p4,w5,p6,w7,p8,c0 c0,w1,p2,w3,n4,w5,p6,w7,n8,c0 c0,w1,p2,w3,p4,w5,n6,w7,n8,c0 c0,w1,n2,w3,n4,w5,n6,w7,n8,c0

5,w1,v2,w3,v4,w5,v6,w7,v8, 6
6,w1,v2,w3,v4,w5,v6,w7,v8, 5

1. 1 sem

d0, 0,d2, 0,d4, 0,d6, 0,c8, 1 d0, 0,l2, 0,l4, 0,l6, 0,c8, 2 l0, 0,d2, 0,d4, 0,d6, 0,c8, 3 l0, 0,l2, 0,l4, 0,l6, 0,c8, 4

1, 0,v2, 0,v4, 0,v6, 0,c8, 2
2, 0,v2, 0,v4, 0,v6, 0,c8, 4
3, 0,v2, 0,v4, 0,v6, 0,c8, 1
4, 0,v2, 0,v4, 0,v6, 0,c8, 3

d0,w1,d2,w3,d4,w5,d6,w7,c8, 1 d0,w1,l2,w3,l4,w5,l6,w7,c8, 2 l0,w1,d2,w3,d4,w5,d6,w7,c8, 3 l0,w1,l2,w3,l4,w5,l6,w7,c8, 4

1,w1,v2,w3,v4,w5,v6,w7,c8, 2
2,w1,v2,w3,v4,w5,v6,w7,c8, 4
3,w1,v2,w3,v4,w5,v6,w7,c8, 1
4,w1,v2,w3,v4,w5,v6,w7,c8, 3

1. 2 sems

1, 0,d2, 0,d4, 0,c6, 0,c8, 1
2, 0,d2, 0,d4, 0,c6, 0,c8, 3
3, 0,l2, 0,l4, 0,c6, 0,c8, 2
4, 0,l2, 0,l4, 0,c6, 0,c8, 4
1, 0,v2, 0,v4, 0,c6, 0,c8, 2
2, 0,v2, 0,v4, 0,c6, 0,c8, 4
3, 0,v2, 0,v4, 0,c6, 0,c8, 1
4, 0,v2, 0,v4, 0,c6, 0,c8, 3

1, 0,d2, 0,c4, 0,d6, 0,c8, 1
2, 0,d2, 0,c4, 0,d6, 0,c8, 3
3, 0,l2, 0,c4, 0,l6, 0,c8, 2
4, 0,l2, 0,c4, 0,l6, 0,c8, 4
1, 0,v2, 0,c4, 0,v6, 0,c8, 2
2, 0,v2, 0,c4, 0,v6, 0,c8, 4
3, 0,v2, 0,c4, 0,v6, 0,c8, 1
4, 0,v2, 0,c4, 0,v6, 0,c8, 3

1,w1,d2,w3,d4,w5,c6,w7,c8, 1
2,w1,d2,w3,d4,w5,c6,w7,c8, 3
3,w1,l2,w3,l4,w5,c6,w7,c8, 2
4,w1,l2,w3,l4,w5,c6,w7,c8, 4
1,w1,v2,w3,v4,w5,c6,w7,c8, 2
2,w1,v2,w3,v4,w5,c6,w7,c8, 4
3,w1,v2,w3,v4,w5,c6,w7,c8, 1
4,w1,v2,w3,v4,w5,c6,w7,c8, 3

1,w1,d2,w3,c4,w5,d6,w7,c8, 1
2,w1,d2,w3,c4,w5,d6,w7,c8, 3
3,w1,l2,w3,c4,w5,l6,w7,c8, 2
4,w1,l2,w3,c4,w5,l6,w7,c8, 4
1,w1,v2,w3,c4,w5,v6,w7,c8, 2
2,w1,v2,w3,c4,w5,v6,w7,c8, 4
3,w1,v2,w3,c4,w5,v6,w7,c8, 1
4,w1,v2,w3,c4,w5,v6,w7,c8, 3

1. 3 sems

1, 0,c2, 0,c2, 0, 6, 0,v8, 2
1, 0,c2, 0,c4, 0,c6, 0,v8, 1
3, 0,c2, 0,c2, 0, 5, 0,v8, 2
3, 0,c2, 0,c4, 0,c6, 0,v8, 1

2, 0, 5, 0, 5, 0,c6, 0,v8, 4
2, 0, 5, 0,c4, 0, 6, 0,v8, 4
2, 0,c2, 0,c4, 0,c6, 0,v8, 3
4, 0, 6, 0, 6, 0,c6, 0,v8, 4
4, 0, 6, 0,c4, 0, 5, 0,v8, 4
4, 0,c2, 0,c4, 0,c6, 0,v8, 3

1,w1,c2,w3,c2,w5, 6,w7,v8, 2
1,w1,c2,w3,c4,w5,c6,w7,v8, 1
3,w1,c2,w3,c2,w5, 5,w7,v8, 2
3,w1,c2,w3,c4,w5,c6,w7,v8, 1

2,w1, 5,w3, 5,w5,c6,w7,v8, 4
2,w1, 5,w3,c4,w5, 6,w7,v8, 4
2,w1,c2,w3,c4,w5,c6,w7,v8, 3
4,w1, 6,w3, 6,w5,c6,w7,v8, 4
4,w1, 6,w3,c4,w5, 5,w7,v8, 4
4,w1,c2,w3,c4,w5,c6,w7,v8, 3

1. 4 sems

1. 4e
2. I w 0 w 0 w 0 w 0 O

1. 0 sems

d0,d1, 0,d3, 0,d5, 0,d7, 0, 1 d0,l1, 0,l3, 0,l5, 0,l7, 0, 2 l0,d1, 0,d3, 0,d5, 0,d7, 0, 3 l0,l1, 0,l3, 0,l5, 0,l7, 0, 4

1,v1, 0,v3, 0,v5, 0,v7, 0, 2
2,v1, 0,v3, 0,v5, 0,v7, 0, 4
3,v1, 0,v3, 0,v5, 0,v7, 0, 1
4,v1, 0,v3, 0,v5, 0,v7, 0, 3

c0,p1, 0,p3, 0,p5, 0,p7, 0,c0 c0,p1, 0,n3, 0,p5, 0,n7, 0,c0 c0,p1, 0,p3, 0,n5, 0,n7, 0,c0 c0,n1, 0,n3, 0,n5, 0,n7, 0,c0

5,v1, 0,v3, 0,v5, 0,v7, 0, 6
6,v1, 0,v3, 0,v5, 0,v7, 0, 5

1. 1 sem

d0,d1, 0,d3, 0,d5, 0,c7, 0, 1 d0,l1, 0,l3, 0,l5, 0,c7, 0, 2 l0,d1, 0,d3, 0,d5, 0,c7, 0, 3 l0,l1, 0,l3, 0,l5, 0,c7, 0, 4

1,v1, 0,v3, 0,v5, 0,c7, 0, 2
2,v1, 0,v3, 0,v5, 0,c7, 0, 4
3,v1, 0,v3, 0,v5, 0,c7, 0, 1
4,v1, 0,v3, 0,v5, 0,c7, 0, 3

1. 2 sems

1,d1, 0,d3, 0,c5, 0,c7, 0, 1
2,d1, 0,d3, 0,c5, 0,c7, 0, 3
3,l1, 0,l3, 0,c5, 0,c7, 0, 2
4,l1, 0,l3, 0,c5, 0,c7, 0, 4
1,v1, 0,v3, 0,c5, 0,c7, 0, 2
2,v1, 0,v3, 0,c5, 0,c7, 0, 4
3,v1, 0,v3, 0,c5, 0,c7, 0, 1
4,v1, 0,v3, 0,c5, 0,c7, 0, 3

1,d1, 0,c3, 0,d5, 0,c7, 0, 1
2,d1, 0,c3, 0,d5, 0,c7, 0, 3
3,l1, 0,c3, 0,l5, 0,c7, 0, 2
4,l1, 0,c3, 0,l5, 0,c7, 0, 4
1,v1, 0,c3, 0,v5, 0,c7, 0, 2
2,v1, 0,c3, 0,v5, 0,c7, 0, 4
3,v1, 0,c3, 0,v5, 0,c7, 0, 1
4,v1, 0,c3, 0,v5, 0,c7, 0, 3

1. 3 sems

1,c1, 0,c1, 0, 6, 0,v7, 0, 2
1,c1, 0,c3, 0,c5, 0,v7, 0, 1
3,c1, 0,c1, 0, 5, 0,v7, 0, 2
3,c1, 0,c3, 0,c5, 0,v7, 0, 1

2, 5, 0, 5, 0,c5, 0,v7, 0, 4
2, 5, 0,c3, 0, 6, 0,v7, 0, 4
2,c1, 0,c3, 0,c5, 0,v7, 0, 3
4, 6, 0, 6, 0,c5, 0,v7, 0, 4
4, 6, 0,c3, 0, 5, 0,v7, 0, 4
4,c1, 0,c3, 0,c5, 0,v7, 0, 3

1. 4 sems

@COLORS 0 0 0 0 1 40 40 40 2 155 195 255 3 80 90 100 4 255 255 255 5 110 100 50 6 220 200 50