FSMgen

Years ago, in need of some state machines, I wrote a script to generate them. They are, after all, tedious to type and more tedious to test. I think this was not too different in spirit from what Cliff Cummings did with "fsm_perl" (fsm_perl: A Script to Generate RTL Code for State Machines and Synopsys Synthesis Scripts, 1999). But what I have is more compact and has several verification and visualization side benefits.
The the essence of an FSM is the set, say M, of 5-tuples (Q, Σ, δ, q₀, F ), specifying little more than:
    • here I am
    • what do I do here?
    • where-can I go & how do I get there?

So why not just type in that smallest bit of information? State machines should not be all about typing. Unless the words like "module", "input", "case", "begin", "end", etc are the names of the states, inputs, outputs, or transition conditions, why type them?
Plus, there are side benefits of using a very compact description such as the one presented below. Most of them derive directly from using a standard from. Some of the benefits are:

    • the automatic analysis and production of a list of all possible paths the state machine can traverse. Such information can be used by verification tools such as Coercion Engine (described elsewhere).
    • it provides hooks in the RTL to capture data at run-time to feed performance analysis tools and visualizers.
    • should you need bubble diagrams, it is trivial to produce an output in a graphics description language, like DOT, and hand that over to a program like Graphviz.
    • the time you save typing can be used to write down assumptions and expectations and intent. And that is a good use of your typing time.

I've make this little write-up because I'm thinking of releasing this tool. Here is FSMgen in brief.

Finite State Machines

Whenever possible, I prefer to write only the essential elements and let generators do the typing. For FSMs, that means creating a file format (.fsm) that contains only inputs, states, transition conditions, and outputs. Here is an example .fsm file, btest.fsm which shows this minimal form. The description here:

NAME=btest
CLK = clk
RESET = reset
ENCODING = BINARY

INITIALSTATE = A
IDLESTATE = A

assign ab = start && !processXdied

A(ab)B
B(bc)C
C(NEXT)D
D(de)E
D(ELSE)F
E(ea)A
F(NEXT)A

waiting <= B
onhold  <= D

is used to generate the Verilog code:

module btest (
  input  clk,
  input  reset,

  input  start,
  input  processXdied,
  input  bc,
  input  de,
  input  ea,

  output onhold,
  output waiting,
  output [2:0] STATE) ;

  localparam A = 3'b000 ;
  localparam B = 3'b001 ;
  localparam C = 3'b010 ;
  localparam D = 3'b011 ;
  localparam E = 3'b100 ;
  localparam F = 3'b101 ;

  wire ab = start && !processXdied ;

  //--------------------------------------------------
  // State driven outputs:
  assign onhold  =  (STATE == D)  ;
  assign waiting =  (STATE == B)  ;

  //--------------------------------------------------
  // Register part of the FSM
  logic [2:0] STATE, nextstate ;

  always @(posedge clk or posedge reset) 
  begin
    if   ( reset ) STATE <= A ;
    else           STATE <= nextstate ;
  end


  //--------------------------------------------------
  // Combinatorial part of the FSM:
  always_comb
  begin
    nextstate = 'bx ;

    case (STATE)
      A : if      (ab) nextstate = B ;
          else         nextstate = A ;

      B : if      (bc) nextstate = C ;
          else         nextstate = B ;

      C :              nextstate = D ;

      D : if      (de) nextstate = E ;
          else         nextstate = F ;

      E : if      (ea) nextstate = A ;
          else         nextstate = E ;

      F :              nextstate = A ;
    endcase
  end
endmodule

Drawing state machines out as bubble diagrams would be fine, if it were just as fast, but I'd still want the source in a form where I can generate more than just RTL. Here is an example of one of the benefits of generating from a compact source like this: automatically creating a list of all possible paths the state machine can take. This is the path information generated from the btest.fsm source above:

BITS=3
CLK=clk
RESET=reset
STATE :: A : 000
STATE :: B : 001
STATE :: C : 010
STATE :: D : 011
STATE :: E : 100
STATE :: F : 101
path1:A(ab)B(bc)C()D(de)E(ea)A
path2:A(ab)B(bc)C()D(ELSE)F()A
path3:A(ab)B(bc)C()D(de)E+(ea)A
path4:A(ab)B+(bc)C()D(de)E(ea)A
path5:A(ab)B+(bc)C()D(ELSE)F()A
path6:A+(ab)B(bc)C()D(de)E(ea)A
path7:A+(ab)B(bc)C()D(ELSE)F()A
path8:A(ab)B+(bc)C()D(de)E+(ea)A
path9:A+(ab)B(bc)C()D(de)E+(ea)A
path10:A+(ab)B+(bc)C()D(de)E(ea)A
path11:A+(ab)B+(bc)C()D(ELSE)F()A
path12:A+(ab)B+(bc)C()D(de)E+(ea)A

The data above can be read by the script Pathmaker.pl which builds acceptor class automata for each path listed. (This is similar to what a simulator working with SystemVerilog concurrent assertions would have to do.) This information is used to verify that a particular path has indeed been taken. Imagine trying to extract the same information from parsing the Verilog directly.
The way to read the path information is best explained by example. Take the path
path5:A(ab)B+(bc)C()D(ELSE)F()A
as the example. An automata built from this, designed to monitor the state machine "btest", will expect the following:

A(ab)B means that from state A the next state in the next clock cycle must be state B. If it transitions to any other state, this particular sequence is not accepted.

B+(bc)C means that from state B next state might be B or C. If it is any other state this particular sequence is not accepted.

C()D means that from state D the next state in the next clock cycle must be state D, and if not this particular sequence is not accepted.

D(ELSE)F means that from state D the next state in the next clock cycle must be F, otherwise this particular sequence is not accepted.

F()A means that from state F the next state in the next clock cycle must be state A, and if not the this particular is not accepted. If it reaches state A, this particular sequence is accepted.

Pathmaker.pl is a tool that creates the acceptor class automata as part of the Coercion Engine (described elsewhere).

The format for .fsm files

Again, I'm trying to stick with inputs, states, transition conditions, and outputs.

Inputs

Inputs come from here: /\s*(CLK|RESET|RESETn|ENCODING|INITIALSTATE|IDLESTATE|INCORPORATE|assign)\s*=\s*(.*)/

The state to state transitions are in the form <STATE>(condition)<OTHERSTATE>. That means that a condition, C, implies creating an input, unless that transition is a lvalue in an assign. In that case the signal becomes an internal wire. For example:

assign ab = inputX && input Y
...
A(ab)B
B(bc)C
...

results in

...
  input inputX,
  input inputY,
  input bc,
...
  assign ab = inputX && input Y ;

States and transition conditions

States and transition conditions come from here: /\s*(.*?)\s*\((.*)\)\s*(\S+)/

There are two keywords in conditions: NEXT and ELSE.
NEXT means always go to the next state. There is no else.
The ELSE keyword replaces an implied else. If you don't specify an ELSE an "else nextstate <= thisstate" is implied. Here are some examples, with comments:

...
A(ab)B       // this is,          if ab, nextstate <= B, else nextstate <= A, implied by omission of an ELSE
B(NEXT)C     // this is,                 nextstate <= C

C(cd)D       // these two become: if cd, nextstate <= D, 
C(ELSE)E     //                   else   nextstate <= E
...

Outputs

Outputs come from here: /\s*(.*?)\s*<=\s+(.*)/

The outputs are derived directly. This

waiting <= B || ThisOtherState && patiently

becomes

assign waiting =  (STATE == B) || (STATE == ThisOtherState) && patiently  ;

ORing is assumed if outputs are repeated as shown below:

A(ab)B
B(NEXT)C
waiting <= B 
...
C(cd)D
C(ELSE)E
waiting <= C

becomes

assign waiting =  (STATE == B) || (STATE == C) ;

Priority, automagic inputs, conditions, Mealy machines, et cetera

NAME= is the name of the module created.

CLK= is the name of the input clock.

RESET= implies an active high reset, while

RESETn= implies an active low reset.

ENCODING= is the type of encoding to use for the state maching. At present it knows the encodings binary, onehot, zerohot. It does Grey, but it doesn't always get it right. I think that's called a "bug".

INITIALSTATE= is the state forced on reset. It can be the same as the IDLESTATE.

IDLESTATE= is the 'return to' state. In order for FSMgen to make the paths, it assumes that there is a loop from the IDLESTATE back to the IDLESTATE. FSMgen currently has some limits in this area. See TODO at the bottom for details.

The script collects all conditions and all rvalues as potential wires. It assumes that if the wire is NOT an lvalue then it's a primary input. The following works too, so one can make Mealy machines:

  ...
#ex:assign someoutput = NamedState  SomeSignal ...
assign Ready = READY && waiting
  ...
READY(...
or
...)READY

becomes

  ...
  input waiting,
  ...
  output Ready,
  ...
  assign Ready = (STATE == READY) && waiting ;
  ...

Regarding priority, just put the state transition lines in order, same as you would in procedural code. In the example below, the conditions from the starting state, HERE, are evaluated in order top-to-bottom:

  ...
HERE(first_this)THAT_STATE
HERE(then_this)THE_OTHER_STATE
HERE(and_this)THE_FINAL_STATE
  ...

becomes

    case (STATE)
     ...
   HERE : 
       if      (first_this) nextstate = THAT_STATE ;
       else if (then_this)  nextstate = THE_OTHER_STATE ;
       else if (and_this)   nextstate = THE_FINAL_STATE ;
       else                 nextstate = HERE ;
     ...

Finally, "//" and "#" are both comment delimiters. "//" style comments are preserved and copied into the output Verilog.

A small example

This is the .fsm description file for the main StreamProcBlank FSM (project described elsewhere). I needed a placeholder state machine for the DUT blank. It took about 3 minutes to write this file:

# This is the main controller state machine for a Stream Processing
# component blank. See StreamProcBlank.sv for details. 
NAME=StreamProcBlank
CLK = clock
RESET = reset
ENCODING = BINARY

INITIALSTATE = INITIAL
IDLESTATE = IDLE

INITIAL (NEXT)     IDLE
IDLE    (!take_it) GIVE_IT
GIVE_IT (take_it)  GOT_IT
GOT_IT  (end_proc) GOOD
GOOD    (thanks)   IDLE

give_it    <= GIVE_IT
start_proc <= GOT_IT
got_it     <= GOT_IT
good       <= GOOD

INCORPORATE=CounterGen(up, Count, clock, reset, start_proc, end_proc, 0, 50)

And one script invocation to get the Verilog code I needed. (Oh. It also comes with a stand-alone SystemVerilog testbench as well as a SystemVerilog interface in case it's needed). The INCORPORATE is an include that calls the CounterGen.pl script. Its function should be obvious. Here is the Verilog:

module StreamProcBlank (
  input  clock,
  input  reset,

  input  take_it,
  input  thanks,

  output give_it,
  output got_it,
  output good,
  output [2:0] STATE) ;

  wire end_proc ;

  localparam INITIAL = 3'b000 ;
  localparam IDLE    = 3'b001 ;
  localparam GIVE_IT = 3'b010 ;
  localparam GOT_IT  = 3'b011 ;
  localparam GOOD    = 3'b100 ;

  //--------------------------------------------------
  // State driven outputs:
  assign give_it    =  (STATE == GIVE_IT) ;
  assign got_it     =  (STATE == GOT_IT) ;
  assign start_proc =  (STATE == GOT_IT) ;
  assign good       =  (STATE == GOOD) ;

  //--------------------------------------------------
  // Register part of the FSM
  logic [2:0] STATE, nextstate ;

  always @(posedge clock or posedge reset) 
  begin
    if   ( reset ) STATE <= INITIAL ;
    else           STATE <= nextstate ;
  end


  //--------------------------------------------------
  // Combinatorial part of the FSM:
  always_comb
  begin
    nextstate = 'bx ;

    case (STATE)
      INITIAL : 
               nextstate = IDLE ;
      IDLE : 
       if      (!take_it) nextstate = GIVE_IT ;
       else               nextstate = IDLE ;

      GIVE_IT : 
       if      (take_it)  nextstate = GOT_IT ;
       else               nextstate = GIVE_IT ;

      GOT_IT : 
       if      (end_proc) nextstate = GOOD ;
       else               nextstate = GOT_IT ;

      GOOD : 
       if      (thanks)   nextstate = IDLE ;
       else               nextstate = GOOD ;
    endcase
  end


  reg  [5:0] Count ;
  always @(posedge clock or posedge reset)
  begin
    if       (reset)     Count <= '0 ;
    else if (start_proc) Count <= (Count == 50) ? '0 : Count + 1 ;
    else                 Count <=  Count ;
  end

  assign end_proc = (Count == 50) ? 1 : 0 ; // Dang. FIXME. Had to add this by hand

endmodule

A savagely long example

This is the .fsm description file for DIP, a state machine used to test the Coercion Engine. DIP stands for Deep, Improbable Path, and the idea here is to create a state machine with a combinatorially improbable state to reach.

# The *purpose* of this state machine is to test the CoercionEngine.
# The CoercionEngine provides a way to dynamically constrain sequences.
# It requires path information, and FSMgen automatically builds directed
# graphs from FSM descriptions, provided they are described in the 
# right format. See the FSMgen format document.
#
# DIP stands for Deep, Improbable Path.
# This is a state machine that is stupidly deep. The probability
# of reaching state J and transitioning to state A is 2^11. 
# If stimulus is allowed to vary randomly, and BTW, there are 10 inputs,
# it might take longer than you want to wait to reach the final
# J->A transition.

NAME = DIP
CLK = clk 
RESET = reset
ENCODING = BINARY

INITIALSTATE = A
IDLESTATE = A

assign ba = !bc_i && (ab_i ||         cd_i || de_i || ef_i || fg_i || gh_i || hi_i || ij_i || ja_i)
assign ca = !cd_i && (ab_i || bc_i ||         de_i || ef_i || fg_i || gh_i || hi_i || ij_i || ja_i)
assign da = !de_i && (ab_i || bc_i || cd_i ||         ef_i || fg_i || gh_i || hi_i || ij_i || ja_i)
assign ea = !ef_i && (ab_i || bc_i || cd_i || de_i ||         fg_i || gh_i || hi_i || ij_i || ja_i)
assign fa = !fg_i && (ab_i || bc_i || cd_i || de_i || ef_i ||         gh_i || hi_i || ij_i || ja_i)
assign ga = !gh_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i ||         hi_i || ij_i || ja_i)
assign ha = !hi_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i ||         ij_i || ja_i)
assign ia = !ij_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i || hi_i ||         ja_i)
assign ja = !ja_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i || hi_i || ij_i        )

A(ab)B

B(ba)A
C(ca)A
D(da)A
E(ea)A
F(fa)A
G(ga)A
H(ha)A
I(ia)A
J(ja)A

B(bc)C
C(cd)D
D(de)E
E(ef)F
F(fg)G
G(gh)H
H(hi)I
I(ij)J


WIP      <= B || C || D || E || F || G || H || I
leaving  <= J

One script invocation produces the Verilog code I need and the path information to give to the Coercion Engine. There are 2044 possible paths for this one. Shown below is the Verilog code then the path information.

module DIP (
  input clk,
  input reset,

  input ab_i,
  input bc_i,
  input cd_i,
  input de_i,
  input ef_i,
  input fg_i,
  input gh_i,
  input hi_i,
  input ij_i,
  input ja_i,

  output WIP,
  output leaving,
  output [3:0] STATE) ;

  localparam A = 4'b0000 ;
  localparam B = 4'b0001 ;
  localparam C = 4'b0010 ;
  localparam D = 4'b0011 ;
  localparam E = 4'b0100 ;
  localparam F = 4'b0101 ;
  localparam G = 4'b0110 ;
  localparam H = 4'b0111 ;
  localparam I = 4'b1000 ;
  localparam J = 4'b1001 ;

  wire ba ;
  wire ia ;
  wire da ;
  wire ha ;
  wire ca ;
  wire fa ;
  wire ja ;
  wire ea ;
  wire ga ;

  assign ba = !bc_i && (ab_i ||         cd_i || de_i || ef_i || fg_i || gh_i || hi_i || ij_i || ja_i) ;
  assign ia = !ij_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i || hi_i ||         ja_i) ;
  assign da = !de_i && (ab_i || bc_i || cd_i ||         ef_i || fg_i || gh_i || hi_i || ij_i || ja_i) ;
  assign ha = !hi_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i ||         ij_i || ja_i) ;
  assign ca = !cd_i && (ab_i || bc_i ||         de_i || ef_i || fg_i || gh_i || hi_i || ij_i || ja_i) ;
  assign fa = !fg_i && (ab_i || bc_i || cd_i || de_i || ef_i ||         gh_i || hi_i || ij_i || ja_i) ;
  assign ja = !ja_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i || gh_i || hi_i || ij_i        ) ;
  assign ea = !ef_i && (ab_i || bc_i || cd_i || de_i ||         fg_i || gh_i || hi_i || ij_i || ja_i) ;
  assign ga = !gh_i && (ab_i || bc_i || cd_i || de_i || ef_i || fg_i ||         hi_i || ij_i || ja_i) ;

  //--------------------------------------------------
  // State driven outputs:
  assign WIP     =  (STATE == B) || (STATE == C) || (STATE == D) || (STATE == E) || (STATE == F) || (STATE == G) || (STATE == H) || (STATE == I)  ;
  assign leaving =  (STATE == J)  ;

  //--------------------------------------------------
  // Register part of the FSM
  logic [3:0] STATE, nextstate ;

  always @(posedge clk or posedge reset)
  begin
    if   ( reset ) STATE <= A ;
    else           STATE <= nextstate ;
  end

  //--------------------------------------------------
  // Combinatorial part of the FSM:
  always_comb
  begin
    nextstate = 'bx ;

    case (STATE)
      A : if     (ab_i) nextstate = B ;
          else          nextstate = A ;

      B : if     (ba)   nextstate = A ;
         else if (bc_i) nextstate = C ;
          else          nextstate = B ;

      C : if     (ca)   nextstate = A ;
         else if (cd_i) nextstate = D ;
          else          nextstate = C ;

      D : if     (da)   nextstate = A ;
         else if (de_i) nextstate = E ;
          else          nextstate = D ;

      E : if     (ea)   nextstate = A ;
         else if (ef_i) nextstate = F ;
          else          nextstate = E ;

      F : if     (fa)   nextstate = A ;
         else if (fg_i) nextstate = G ;
          else          nextstate = F ;

      G : if     (ga)   nextstate = A ;
         else if (gh_i) nextstate = H ;
          else          nextstate = G ;

      H : if     (ha)   nextstate = A ;
         else if (hi_i) nextstate = I ;
          else          nextstate = H ;

      I : if     (ia)   nextstate = A ;
         else if (ij_i) nextstate = J ;
          else          nextstate = I ;

      J : if     (ja)   nextstate = A ;
          else          nextstate = J ;

    endcase
  end
endmodule

BITS=4
CLK=clk
RESET=reset
STATE :: A : 0000
STATE :: B : 0001
STATE :: C : 0010
STATE :: D : 0011
STATE :: E : 0100
STATE :: F : 0101
STATE :: G : 0110
STATE :: H : 0111
STATE :: I : 1000
STATE :: J : 1001
path1:A(ab)B(ba)A
path2:A(ab)B(bc)C(ca)A
path3:A(ab)B+(ba)A
path4:A+(ab)B(ba)A
path5:A(ab)B(bc)C(cd)D(da)A
path6:A(ab)B(bc)C+(ca)A
path7:A(ab)B+(bc)C(ca)A
path8:A+(ab)B(bc)C(ca)A
path9:A+(ab)B+(ba)A
path10:A(ab)B(bc)C(cd)D(de)E(ea)A
path11:A(ab)B(bc)C(cd)D+(da)A
path12:A(ab)B(bc)C+(cd)D(da)A
path13:A(ab)B+(bc)C(cd)D(da)A
path14:A(ab)B+(bc)C+(ca)A
path15:A+(ab)B(bc)C(cd)D(da)A
path16:A+(ab)B(bc)C+(ca)A
path17:A+(ab)B+(bc)C(ca)A
path18:A(ab)B(bc)C(cd)D(de)E(ef)F(fa)A
path19:A(ab)B(bc)C(cd)D(de)E+(ea)A
path20:A(ab)B(bc)C(cd)D+(de)E(ea)A
path21:A(ab)B(bc)C+(cd)D(de)E(ea)A
path22:A(ab)B(bc)C+(cd)D+(da)A
path23:A(ab)B+(bc)C(cd)D(de)E(ea)A
path24:A(ab)B+(bc)C(cd)D+(da)A
path25:A(ab)B+(bc)C+(cd)D(da)A
path26:A+(ab)B(bc)C(cd)D(de)E(ea)A
path27:A+(ab)B(bc)C(cd)D+(da)A
path28:A+(ab)B(bc)C+(cd)D(da)A
path29:A+(ab)B+(bc)C(cd)D(da)A
path30:A+(ab)B+(bc)C+(ca)A
path31:A(ab)B(bc)C(cd)D(de)E(ef)F(fg)G(ga)A
path32:A(ab)B(bc)C(cd)D(de)E(ef)F+(fa)A
path33:A(ab)B(bc)C(cd)D(de)E+(ef)F(fa)A
path34:A(ab)B(bc)C(cd)D+(de)E(ef)F(fa)A
path35:A(ab)B(bc)C(cd)D+(de)E+(ea)A
path36:A(ab)B(bc)C+(cd)D(de)E(ef)F(fa)A
path37:A(ab)B(bc)C+(cd)D(de)E+(ea)A
path38:A(ab)B(bc)C+(cd)D+(de)E(ea)A
path39:A(ab)B+(bc)C(cd)D(de)E(ef)F(fa)A
path40:A(ab)B+(bc)C(cd)D(de)E+(ea)A
path41:A(ab)B+(bc)C(cd)D+(de)E(ea)A
path42:A(ab)B+(bc)C+(cd)D(de)E(ea)A
path43:A(ab)B+(bc)C+(cd)D+(da)A
path44:A+(ab)B(bc)C(cd)D(de)E(ef)F(fa)A
path45:A+(ab)B(bc)C(cd)D(de)E+(ea)A
path46:A+(ab)B(bc)C(cd)D+(de)E(ea)A
path47:A+(ab)B(bc)C+(cd)D(de)E(ea)A
path48:A+(ab)B(bc)C+(cd)D+(da)A
path49:A+(ab)B+(bc)C(cd)D(de)E(ea)A
path50:A+(ab)B+(bc)C(cd)D+(da)A
path51:A+(ab)B+(bc)C+(cd)D(da)A
path52:A(ab)B(bc)C(cd)D(de)E(ef)F(fg)G(gh)H(ha)A
path53:A(ab)B(bc)C(cd)D(de)E(ef)F(fg)G+(ga)A
path54:A(ab)B(bc)C(cd)D(de)E(ef)F+(fg)G(ga)A
path55:A(ab)B(bc)C(cd)D(de)E+(ef)F(fg)G(ga)A
path56:A(ab)B(bc)C(cd)D(de)E+(ef)F+(fa)A
path57:A(ab)B(bc)C(cd)D+(de)E(ef)F(fg)G(ga)A
path58:A(ab)B(bc)C(cd)D+(de)E(ef)F+(fa)A
path59:A(ab)B(bc)C(cd)D+(de)E+(ef)F(fa)A
path60:A(ab)B(bc)C+(cd)D(de)E(ef)F(fg)G(ga)A
path61:A(ab)B(bc)C+(cd)D(de)E(ef)F+(fa)A
path62:A(ab)B(bc)C+(cd)D(de)E+(ef)F(fa)A
path63:A(ab)B(bc)C+(cd)D+(de)E(ef)F(fa)A
path64:A(ab)B(bc)C+(cd)D+(de)E+(ea)A
path65:A(ab)B+(bc)C(cd)D(de)E(ef)F(fg)G(ga)A
path66:A(ab)B+(bc)C(cd)D(de)E(ef)F+(fa)A
path67:A(ab)B+(bc)C(cd)D(de)E+(ef)F(fa)A
path68:A(ab)B+(bc)C(cd)D+(de)E(ef)F(fa)A
path69:A(ab)B+(bc)C(cd)D+(de)E+(ea)A
path70:A(ab)B+(bc)C+(cd)D(de)E(ef)F(fa)A
path71:A(ab)B+(bc)C+(cd)D(de)E+(ea)A
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path1997:A+(ab)B(bc)C(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
path1998:A+(ab)B(bc)C+(cd)D(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
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path2003:A+(ab)B(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I(ij)J+(ja)A
path2004:A+(ab)B(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J(ja)A
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path2010:A+(ab)B+(bc)C(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I(ij)J+(ja)A
path2011:A+(ab)B+(bc)C(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J(ja)A
path2012:A+(ab)B+(bc)C+(cd)D(de)E(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
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path2014:A+(ab)B+(bc)C+(cd)D(de)E+(ef)F+(fg)G(gh)H+(hi)I+(ij)J+(ja)A
path2015:A+(ab)B+(bc)C+(cd)D(de)E+(ef)F+(fg)G+(gh)H(hi)I+(ij)J+(ja)A
path2016:A+(ab)B+(bc)C+(cd)D(de)E+(ef)F+(fg)G+(gh)H+(hi)I(ij)J+(ja)A
path2017:A+(ab)B+(bc)C+(cd)D(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J(ja)A
path2018:A+(ab)B+(bc)C+(cd)D+(de)E(ef)F(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
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path2022:A+(ab)B+(bc)C+(cd)D+(de)E(ef)F+(fg)G+(gh)H+(hi)I+(ij)J(ja)A
path2023:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F(fg)G(gh)H+(hi)I+(ij)J+(ja)A
path2024:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F(fg)G+(gh)H(hi)I+(ij)J+(ja)A
path2025:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F(fg)G+(gh)H+(hi)I(ij)J+(ja)A
path2026:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F(fg)G+(gh)H+(hi)I+(ij)J(ja)A
path2027:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G(gh)H(hi)I+(ij)J+(ja)A
path2028:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G(gh)H+(hi)I(ij)J+(ja)A
path2029:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G(gh)H+(hi)I+(ij)J(ja)A
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path2032:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I(ij)J(ja)A
path2033:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ia)A
path2034:A(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
path2035:A+(ab)B(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
path2036:A+(ab)B+(bc)C(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
path2037:A+(ab)B+(bc)C+(cd)D(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
path2038:A+(ab)B+(bc)C+(cd)D+(de)E(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A
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path2040:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G(gh)H+(hi)I+(ij)J+(ja)A
path2041:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H(hi)I+(ij)J+(ja)A
path2042:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I(ij)J+(ja)A
path2043:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J(ja)A
path2044:A+(ab)B+(bc)C+(cd)D+(de)E+(ef)F+(fg)G+(gh)H+(hi)I+(ij)J+(ja)A

TODO

[ ] Fix the broken Grey coding encoding option.
[ ] Now that I know what I want it to do, specify it properly. This includes better cycle detection and will allow wider range of FSMs to be generated.
[ ] Converting it from Perl to C++. There are some graph algorithms already written in C++ for walking directed graphs and cycle detection that I can use.