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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.
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
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
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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(
draw pda for l={an,bm,an/m,n>=0} n is in superscript
This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.
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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
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Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
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