HW3Answers - CS 341 Automata Theory Elaine Rich Homework 3...

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CS 341 Automata Theory Elaine Rich Homework 3 Answers 1. Construct a deterministic finite state machine to accept each of the following languages: a) The set of binary representations, without leading 0’s, of integers that are divisible by 4. b) The set of binary representations, without leading 0’s, of integers that are powers of 4. c) The set of binary strings that have at least one occurrence of the substring 001. d) The set of binary strings that have no substring 001.
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e) The set of binary strings with at most one pair of consecutive 0’s and at most one pair of consecutive 1’s. f) The set of all binary strings with the property that none of its prefixes ends in 0. g) {w is an element of {a, b}*: # a w + 2# b w is divisible by 5}. (# a w is the number of occurrences of the symbol a in w).
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2. Construct a nondeterministic finite state machine to accept each of the following languages: a) { a n ba m : n, m ≥ 0, n ≡ 3 m} b) The set of binary strings that contain both substrings 101 and 010.
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3. Let L be a subset of Σ*. Define the following languages. Pref (L) = {w is an element of Σ*: x=wy for some x an element of L, y element of Σ*} (The prefixes of L) Suf (L) = {w is an element of Σ*: x=yw for some x an element of L, y element of Σ*} (The suffixes of L) Max (L) = {w is an element of L: if x ≠ ε then wx is not an element of L} Show that if L is accepted by some finite automaton, then so is each of the
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This note was uploaded on 12/03/2009 for the course CS 341 taught by Professor Rich during the Fall '08 term at University of Texas.

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HW3Answers - CS 341 Automata Theory Elaine Rich Homework 3...

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