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Course: CSC 236, Fall 2009
School: Toledo
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/ CSC236 Introduction to the Theory of Computation Homework #2 Due date: August 8 Part 1 1. For each of the following languages over the alphabet = {0, 1}, dene a regular expression that accepts the language. (a) L1 = {x | x contains the substring 01001} (b) L2 = {x | x contains an even number of 0s and an even number of 1s} (c) L3 = {x | x contains a substring of length at most 5 that has at least three 1s} 2....

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/ CSC236 Introduction to the Theory of Computation Homework #2 Due date: August 8 Part 1 1. For each of the following languages over the alphabet = {0, 1}, dene a regular expression that accepts the language. (a) L1 = {x | x contains the substring 01001} (b) L2 = {x | x contains an even number of 0s and an even number of 1s} (c) L3 = {x | x contains a substring of length at most 5 that has at least three 1s} 2. For each language in question 1, dene a deterministic nite state automaton that accepts the language. 3. For a language L over an alphabet , let L(2) denote the following language over 2 : L(2) = {(x1 , y1 ) (xn , yn ) | either x1 xn L or y1 yn L} Prove that if L is a regular language, then L(2) is a regular language. Part 2 4. In this question we consider deterministic nite automata which are augmented with a nite memory which, for some constant m N, stores the last m input symbols that were We read. shall call such an automaton a DFSA-M. A DFSA-M is a tuple (Q, , , s0 , F, m, M, {fq | q M }), where Q, , , s0 , F are as in the denition of a DFSA, and m N is the size of the memory M Q is a set of special function states For each function state q M there is a function fq : m Q The computation of a DFSA-M is the same as the computation of a DFSA, with the following exception: if the DFSA-M enters a function state q M , and x1 , . . . , xm are the last m symbols read by the automaton, then the automaton immediately enters the sta...

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