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Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q0, Fi where Q, Σ, q0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}).
We must also modify the de?nitions of the directly computes relation and the path function to allow for the possibility that ε-transitions may occur anywhere in a computation or path. The ε-transition from state 1 to state 3 in the example, for instance, allows the automaton on input ‘a' to go from state 0 not only to state 1 but also to immediately go on to state 3. Similarly, it allows the automaton, when in state 1 with input ‘b', to move ?rst to state 3 and then take the ‘b' edge to state 0 or, when in state 0 with input ‘a', to move ?rst to state 2 and then take the ‘a' edge to state 3. Thus, on a given input ‘σ', the automaton can take any sequence of ε-transitions followed by exactly one σ-transition and then any sequence of ε-transitions. To capture this in the de?nition of δ we start by de?ning the function ε-Closure which, given a state, returns the set of all states reachable from it by any sequence of ε-transitions.
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
Define the following concept with an example: a. Ambiguity in CFG b. Push-Down Automata c. Turing Machine
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We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one
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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
1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program
design a turing machine that accepts the language which consists of even number of zero''s and even number of one''s?
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