Strictly local languages, Theory of Computation

Assignment Help:

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.


Related Discussions:- Strictly local languages

Strictly local languages, We have now de?ned classes of k-local languages f...

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

Strictly 2-local languages, The fundamental idea of strictly local language...

The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan

Discrete math, Find the Regular Grammar for the following Regular Expressio...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Can you help me in automata questions, i have some questions in automata, c...

i have some questions in automata, can you please help me in solving in these questions?

Complement - operations on languages, The fact that SL 2 is closed under i...

The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that

Formal language theory, This was one of the ?rst substantial theorems of Fo...

This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But

Path function of a nfa, The path function δ : Q × Σ* → P(Q) is the extensio...

The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l

Overview of dfa, Explain Theory of Computation ,Overview of DFA,NFA, CFG, P...

Explain Theory of Computation ,Overview of DFA,NFA, CFG, PDA, Turing Machine, Regular Language, Context Free Language, Pumping Lemma, Context Sensitive Language, Chomsky Normal For

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd