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The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings:
Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an NFA with ε-transitions start by ?nding the set of states reachable from q using only ε-transitions and then, for each symbol σ of w (in order) ?nd the set of states reachable from those by an edge labeled σ and then the set of states reachable from those by any sequence of ε-transitions, etc.
Nothing else in the de?nitions need change. The automaton still accepts w if there is any computation on (q0,w) that terminates in a ?nal state after scanning the entire input. Equivalently, it accepts w if there is a path labeled w from the initial state to a ?nal state, which is to say, if δ(q0,w) includes any member of F. Note that the automaton of the example above will accept ‘ε' since state 2 is in ε-Closure(0) and, therefore in δ(0, ε).
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular
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Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
Prepare the consolidated financial statements for the year ended 30 June 2011. On 1 July 2006, Mark Ltd acquired all the share capitall of john Ltd for $700,000. At the date , J
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