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The SL2 languages are speci?ed with a set of 2-factors in Σ2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and end of the string, respectively), the recognizable languages are speci?ed with triples in Q × Q × Σ (along with an indication of the start and accepting states). In studying the SL languages, it was useful to consider those factors as tiles, allowing us to generate strings in the language recognized by the SL-automaton by laying them out in overlapping sequences. We can develop a similar generator model from our FSAs by extending the triples of the edge relation with triples from {?}×Q×{?} (to designate starting tiles)
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
What is the purpose of GDTR?
1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage 2. Prove the following language is non-Turing recognizable using the diagnolization
Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to
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.
Let ? ={0,1} design a Turing machine that accepts L={0^m 1^m 2^m } show using Id that a string from the language is accepted & if not rejected .
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.
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