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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 r
For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as the
Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica
Let L1 and L2 be CGF. We show that L1 ∩ L2 is CFG too. Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the sec
The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
unification algorithm
A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note
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
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