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

Turing machine, Can v find the given number is palindrome or not using turi...

Can v find the given number is palindrome or not using turing machine

Mapping reducibility, (c) Can you say that B is decidable? (d) If you someh...

(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?

Decision problems, In Exercise 9 you showed that the recognition problem an...

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

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

The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an

Kleene closure, So we have that every language that can be constructed from...

So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r

Local suffix substitution closure, The k-local Myhill graphs provide an eas...

The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo

Class of local languages is not closed under union, Both L 1 and L 2 are ...

Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con

Chomsky normal form, s->0A0|1B1|BB A->C B->S|A C->S|null find useless symbo...

s->0A0|1B1|BB A->C B->S|A C->S|null find useless symbol?

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