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While the SL2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless-the behavior of the automaton depends only on the most recent symbol it has read.
Certainly there are many languages of interest that are not SL2, that will require a more sophisticated algorithm than strictly 2-local automata.
One obvious way of extending the SL2 automata is to give them more memory. Consider, for instance, the language of algebraic expressions over decimal integer constants in which we permit negative constants, indicated by a pre?x ‘-'. Note that this is not the same as allowing ‘-' to be used as a unary operator. In the latter case we would allow any number of ‘-'s to occur in sequence (indicating nested negation), in the case in hand, we will allow ‘-'s to occur only singly (as either a subtraction operator or a leading negative sign) or in pairs (as a subtraction operator followed by a leading negative sign). We will still forbid embedded spaces and the use of ‘+' as a sign.
This is not an SL2 language. If we must permit ‘--' anywhere, then we would have to permit arbitrarily long sequences of ‘-'s. We can recognize this language, though, if we widen the automaton's scanning window to three symbols.
The key thing about the Suffx Substitution Closure property is that it does not make any explicit reference to the automaton that recognizes the language. While the argument tha
Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1 and G2. The two grammars can be shown to
construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.
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Question 2 (10 pt): In this question we look at an extension to DFAs. A composable-reset DFA (CR-DFA) is a five-tuple, (Q,S,d,q0,F) where: – Q is the set of states, – S is the alph
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