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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.
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1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage 2. Prove the following language is non-Turing recognizable using the diagnolization
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how to find whether the language is cfl or not?
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general. De?nition (Strictly Local Languages) A langu
This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.
1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program
Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev
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