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unquoted occurrence of a symbol from the set  , then that symbol must occur in either the first or last position to be interpreted; otherwise  or  is treated simply as a null symbol without function or interpretation. If I1 contains more than one unquoted occurrence of symbols from the set then only the leftmost is operative and then only if it occupies the first position. For type 4 the same convention applies to I2, with the additional stipulation that, if the operative symbol is the same in both I1 and I2, then only the occurrence in I1 is interpreted. Similarly, for types 1 through 4, only the leftmost occurrence of an unquoted  is operative. Moreover, if , , or occur unquoted in the output signal of the broadcast unit without interpretable occurrences in the arguments, they are once again treated as null symbols (and are not broadcast). Thus the broadcast unit  "looks for" any signal with a 4 symbol suffix beginning with 11 and ending in 0; for example, the signal 001110 would yield the output 111 one time-step later. |
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The final source of ambiguity arises when two or more signals satisfy the same argument of a given string-processing broadcast unit. For example, when the state is |
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the broadcast unit *11: could process either 11 or 1100, producing either the output 1 or else the output 00. This difficulty is resolved by having the unit select one of the two signals at random. That is, if there are c signals satisfying a given argument at time t,then each is assigned a probability 1/c and one is chosen at random under this distribution. This method of resolving the difficulty extends the power of the language, allowing the representation of random processes. |
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The following examples exhibit typical constructions and operations within the "broadcast language": |
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1. The object is to produce the concatenation of two arbitrary persistent strings uniquely identified by the prefixes I1and I2respectively. In so doing the prefixes should be dropped and the result should be identified by the new prefix I3. This is accomplished by the broadcast unit |
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2. The object is to generate a sample of the random variable defined by assigning probability 1/n to each of the numbers {1, 2, . . , n}. To do this each |
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