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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 alphabet. The automaton starts with the window positioned over the beginning of string marker and the first symbol of the word (if any). At each step, it looks up the pair of symbols in the window in a table of pairs of symbols. It halts when the end of string marker is in the window (if not sooner).
The S-R element is a set/reset latch. It holds the current output which is initially set to TRUE by driving the START input FALSE. (The inverting circle and vinculum over the signal name indicate an input that is activated when it is driven FALSE.) It is then is reset to FALSE if any pair of symbols in the window fails to match some pair in the lookup table (if output of the ‘∈' element ever goes FALSE). Once reset it remains FALSE. Since the output will be FALSE at the end of the string if it ever goes FALSE during the computation, we may just as well assume that the automaton halts when the first pair that is not in the lookup table is encountered.
Formally, all we need do to specify a particular instance of a strictly 2-local automaton is to give the alphabet and list the pairs of symbols in the internal table.
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
designing DFA
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
Myhill graphs also generalize to the SLk case. The k-factors, however, cannot simply denote edges. Rather the string σ 1 σ 2 ....... σ k-1 σ k asserts, in essence, that if we hav
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
constract context free g ={ a^n b^m : m,n >=0 and n
We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also
Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
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
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