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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 recognizable languages that cannot be constructed in this way. The one fundamental operation that LTO was not closed under was Kleene closure. It's worth asking, then, how the class of recognizable languages fairs under Kleene closure.
examples of decidable problems
The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p
value chain
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
De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p
The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
unification algorithm
LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl
The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that
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