sol06 - CS 154 Intro. to Automata and Complexity Theory...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 154 Intro. to Automata and Complexity Theory Handout 38 Autumn 2009 David Dill December 4, 2008 Solution Set 7 Problem 1 There is no reliable method for doing this, but you can Fgure it out from examples (see how the book does it for expression grammars). The sentence symbol is R : R R + P | P P P · K | K K K ∗ | ( R ) |∅| e | a | b R P K K * ( R ) R + P P P . K K a K a b Problem 1’ A string is not of the form ww if it is of odd length, or (if | w | = n ) there is a mismatch at positions i and n + i where 1 i n . The second condition is the hardest to Fgure out. However, suppose the string has even length, so it can be written as ww where | w | = | w | . If w n = w then w = xcy and w = x dy where the only conditions on x , y , x , y are arbitrary strings over { a,b } where | x | = | x | and | y | = | y | and c,d ∈ { a,b } and c n = d . | yx | is of length | x | + | y | = | x | + | y | , so we can divide ww di±erently, into 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
strings xcu and vdy where uv = yx and | u | = | x | and | v | = | y | . xcu and vdy are thus any strings of odd length whose middle symbols diFer. Here is a C±G: A aAa | aAb | bAa | bAb | a B aBa | aBb | bBa | bBb | b S A | B | AB | BA S is the sentence symbol. The strings derived from A are all the odd-length strings with
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

sol06 - CS 154 Intro. to Automata and Complexity Theory...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online