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CSCI 3130: Formal languages and automata theory

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❶Homework 3 Solution Set C or better in Algorithms CS:
## Theory of Computation, Homework 3 Sample Solution

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The Circuit Value Problem. A The KnasterTarski Theorem. Hints and Solutions More on the PolynomialTime Hierarchy. Complexity of Primality Testing. Hints for Selected Miscellaneous Exercises. Solutions to Selected Miscellaneous Exercises. Constructing an NFA with epsilon transitions from a regular expression. Constructing a regular expression for the language accepted by a DFA. Equivalence of regular expressions and DFAs. Summary of five alternative representations for regular languages.

Closure of regular sets under union, intersection, complementation, finite number of Boolean operations. Pumping Lemma for regular languages. More on Pumping Lemma. Proving languages non-regular using Pumping Lemma. Substitution as an operation to map symbols, strings and languages in one alphabet to languages in another alphabet. Substitution of regular languages. Closure of regular languages under substitution.

Proving regular expression identities using substitution. Closure of regular languages under homomorphism and inverse homomorphism. More on inverse homomorphism. Proving non-regularity of languages using closure results. Reasoning about emptiness and finiteness of regular languages. Quotients of regular languages with arbitrary languages. Reasoning about the minimum number of states needed to recognize a regular language.

The beauty of Myhill-Nerode Theorem. Proving languages regular and non-regular using Myhill-Nerode Theorem. Intuition behind minimization of DFA. Uniqueness upto isomorphism of the minimized DFA for a given regular language. Use in checking equality of languages. Derivation of strings from non-terminals. Leftmost and rightmost derivations. Parse trees as capturing all derivation sequences. Removing ambiguity in specific cases.

Ambiguous grammars for arithmetic expressions. Effect of grammar ambiguity on interpretation of arithmetic expressions. Modifying grammars to enforce operator precedence in arithmetic expressions. Our Theory of Computation Assignment help tutors help with topics like grammars and machines, Chomsky hierarchy, decidability;Models of computation such as Turing machines, RAM machines, Markov algorithms, Post systems, recursive functions, lambda-calculus; Computability: Some of the Theory of Computation assignments help topics include: We help with topics like properties of r.

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