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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.
Perfect shuffle permutation
When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one
The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular
examples of decidable problems
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
Define the following concept with an example: a. Ambiguity in CFG b. Push-Down Automata c. Turing Machine
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
phases of operational reaserch
The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations
Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode
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