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De?nition (Instantaneous Description) (for both DFAs and NFAs)
An instantaneous description of A = (Q,Σ, δ, q0, F), either a DFA or an NFA, is a pair hq,wi ∈ Q×Σ*, where q the current state and w is the portion of the input under and to the right of the read head.
The directly computes relation is also the same.
De?nition (Directly Computes Relation) (for both DFAs and NFAs without ε-transitions).
Note that while this is de?ned identically for both DFAs and NFAs, in the case of NFAs it is no longer even partial functional; an ID may well have many successors. Moreover, it is no longer true that the only IDs without successors are those in which w = ε. The effect of this is that the transition function (δ(q, σ)) as we de?ned it earlier is no longer total or even functional: there may be some q and σ for which δ(q, σ) is not de?ned (in notation: δ(q, σ)↑) and there may be some q and σ for which there are multiple states which could be the value of δ(q, σ). We can accommodate both of these possibilities by taking the transition function for NFAs to be a function returning a set of states.
State and Prove the Arden's theorem for Regular Expression
how to understand DFA ?
When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is
Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be
Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
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
how to find whether the language is cfl or not?
RESEARCH POSTER FOR MEALY MACHINE
The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive
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