Name
Abstract | ||
|---|---|---|
Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values arc updated in the following way: Os are changed to Is at all positions where the value to the right is a 1, while Is arc changed to Os at all positions where the values to the left and right arc both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern. and a repeating right pattern. which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state. and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods 121 have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.4204/EPTCS.1.4 | ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE |
Keywords | Field | DocType |
automata theory,cellular automaton,formal language,computational complexity,polynomial time,turing machine | Discrete mathematics,Probabilistic Turing machine,Universal Turing machine,Computer science,Algorithm,Turing reduction,Turing machine,Turing machine examples,Alternating Turing machine,Non-deterministic Turing machine,Rule 110 | Journal |
Volume | Issue | ISSN |
1 | 1 | 2075-2180 |
Citations | PageRank | References |
5 | 0.51 | 5 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthew Cook | 1 | 100 | 10.77 |