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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.
The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.
Construct a PDA that accepts { x#y | x, y in {a, b}* such that x ? y and xi = yi for some i, 1 = i = min(|x|, |y|) }. For your PDA to work correctly it will need to be non-determin
Explain the Chomsky's classification of grammar
We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
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
Automata and Compiler (1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last f
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
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