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One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define particular, given languages. Towards that end, note that a strictly 2-local automaton can require a particular symbol to appear at the beginning or end of the string and it can permit particular pairs of symbols to occur in the interior of the string but, in general, it can't require an arbitrary pair of symbols to occur in the interior of the string. Consider, for example the language:
This is just the set of all strings over {a, b} in which the sequence ‘ab' occurs at least once. Since the string aabaa is in L1, any strictly 2-local automaton will have to include at least the pairs:
fia, aa, ab, ba, afi.
But then the string aaaaa will also be accepted, using just the first two and the last one of these pairs. Roughly, as long as we have to permit other pairs starting with ‘a' we cannot require ‘ab' to occur.
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici
A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of
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