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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.
conversion from nfa to dfa 0 | 1 ___________________ p |{q,s}|{q} *q|{r} |{q,r} r |(s) |{p} *s|null |{p}
Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.
Computations are deliberate for processing information. Computability theory was discovered in the 1930s, and extended in the 1950s and 1960s. Its basic ideas have become part of
The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive
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
how to write program Minimum Cost Calculation - Vogel Approximation Method(VAM
A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
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
s-> AACD A-> aAb/e C->aC/a D-> aDa/bDb/e
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