Understanding Computation (46 page)
Now we can put everything together to implement an overall#to_cyclicmethod for aTagRulebook, then use it in aTagSystem#to_cyclicmethod that converts both
the rulebook and the current string to yield a complete cyclic tag
system:
classTagRulebookdefto_cyclic(encoder)CyclicTagRulebook.new(cyclic_rules(encoder)+cyclic_padding_rules(encoder))endendclassTagSystemdefto_cyclicTagSystem.new(encoder.encode_string(current_string),rulebook.to_cyclic(encoder))endend
Here’s what happens when we convert our number-incrementing tag
system and run it:
>>cyclic_system=system.to_cyclic=> #>>cyclic_system.run100010000100010001000100(aabbbb)000100001000100010001000010001000010001001000010001000100010000100010000100010100001000100010001000010001000010001100001000100010001000010001000010001(abbbbccdd)00001000100010001000010001000010001000100010001000100001000100001000100100010001000100001000100001000101000100010001000010001000010001(bbbbccdd)1000100010001000010001000010001000100010001000010001000010001000100010010001000100001000100001000100010001010001000100001000100001000100010001(bbbccdddd)10001000100001000100001000100010001000100010000100010000100010001000100100010000100010000100010001000101000100001000100001000100010001(bbccdddd)1000100001000100001000100010001000100001000100001000100010001000100010010000100010000100010001000100010001010000100010000100010001000100010001(bccdddddd)10000100010000100010001000100010001000010001000010001000100010001000100010001000010001000100010001000100100010000100010001000100010001(ccdddddd)010001000010001000100010001000110001000010001000100010001000100010000100010001000100010001⋮
001011=> nil
The encoded version of the tag system’s
arule kicks in here.
The first full character of the simulated string has been
processed, so the following four steps use blank rules to delete the
next simulated character.
After eight steps of the cyclic tag system, one full step of the
simulated tag system is complete.
The encoded
brule is
triggered here…
…and again here.
Twenty-four steps into the cyclic tag system computation, and we
reach the representation of the simulated tag system’s final string,ccdddddd.The simulated tag system has no rules for strings beginning with
cord, so the cyclic tag system’s current string
keeps getting shorter and shorter…
…until it becomes empty, and the system halts.