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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 language accepted by a NFA A = (Q,Σ, δ, q 0 , F) is NFAs correspond to a kind of parallelism in the automata. We can think of the same basic model of automaton: an inpu
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
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
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
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima
let G=(V,T,S,P) where V={a,b,A,B,S}, T={a,b},S the start symbol and P={S->Aba, A->BB, B->ab,AB->b} 1.show the derivation sentence for the string ababba 2. find a sentential form
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat
examples of decidable problems
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