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Theory of Computation
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Module 1
Proof Techniques for Regular Languages
1
Constructing and Proving Product DFAs for Boolean Language Combinations
Construct a product DFA for a Boolean combination of two regular languages and prove its correctness.
Construct a product DFA for a Boolean combination of two regular languages and prove its correctness.
2
Proving Nonregularity with the Pumping Lemma
Prove that a language is nonregular using the pumping lemma for regular languages.
Prove that a language is nonregular using the pumping lemma for regular languages.
3
Proving Nonregularity Using Closure Properties
Prove that a language is nonregular by combining closure properties with a known nonregular language.
Prove that a language is nonregular by combining closure properties with a known nonregular language.
4
Proving DFA State Lower Bounds with Pairwise Distinguishable Strings
Use pairwise distinguishable strings to prove a Myhill–Nerode lower bound on the number of DFA states.
Use pairwise distinguishable strings to prove a Myhill–Nerode lower bound on the number of DFA states.
5
Proving DFA Minimality: Reachability and State Distinguishability
Prove that a given DFA is minimal by establishing reachability and pairwise distinguishability of its states.
Prove that a given DFA is minimal by establishing reachability and pairwise distinguishability of its states.
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