automata, Theory of Computation

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Deterministic finite automata, conversion from nfa to dfa 0 | 1 ____...

conversion from nfa to dfa 0 | 1 ___________________ p |{q,s}|{q} *q|{r} |{q,r} r |(s) |{p} *s|null |{p}

Finite languages and strictly local languages, Theorem The class of ?nite l...

Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N

Formal language theory, This was one of the ?rst substantial theorems of Fo...

This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But

Find a regular expression, Find a regular expression for the regular langua...

Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}

Graph Connectivity, Let G be a graph with n > 2 vertices with (n2 - 3n + 4)...

Let G be a graph with n > 2 vertices with (n2 - 3n + 4)/2 edges. Prove that G is connected.

Non-regular languages, Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = ...

Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn

Path function of a nfa, The path function δ : Q × Σ* → P(Q) is the extensio...

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

Myhill-nerode, Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff...

Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn

Finite-state automaton, Paths leading to regions B, C and E are paths which...

Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no

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