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Let = {0,1}. Let WWk = {ww| w and w is of length k}. a.

Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser ISBN: 9781133187790 221

Solution for problem 1.69 Chapter 1

Introduction to the Theory of Computation | 3rd Edition

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Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser

Introduction to the Theory of Computation | 3rd Edition

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Problem 1.69

Let = {0,1}. Let WWk = {ww| w and w is of length k}. a. Show that for each k, no DFA can recognize WWk with fewer than 2k states. b. Describe a much smaller NFA for WWk, the complement of WWk.

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March 24, 2016  Extra credit assignment o Analyze one of four articles o Pick out statements regarding geology or paleontology o Ask  It is logical  Can this be substantiated o Write a paper that is more than one page but not more than three, single spaced o Include references  Reference the source of the factual information of your paper  Have a bibliography  Must use at least two scientific sources o Make sure that you use scientific names of animals correctly  Name of genus is always capitalized, name of species is never capitalized  Genus and species names must either be italicized or underlined  Late Triassic (archosaur) o Archosaurs include crocodilians, flying reptiles, dinosaurs and dinosaurian  All of the reptiles were relatively small, bipedal and quadrupedal carnivores o Only 8% of archosaurs are dinosaurs o End Triassic extinction event  Wipes out a lot of the archosaurs  Dinosaurs are allowed to radiate and take over  Jurassic and Cretaceous o The big terrestrial animals  Don’t swim in the water or fly in the air yet o Largest animals that ever lived were dinosaurs o Two different varieties  Saurischia  Herbivores  Carnivores  Ornithischia  Herbivores  Ischia means hip  Saur means lizard  Ornith means bird  Lizard and bird dinosaurs o Pelvis is very involved in a lot of the changes of dinosaurs  Bone on top called the ilium  Bone hanging down the front called the pubis  Bone hanging down the back called the ischium  Opening that is formed by all three bones  Where the hind leg fits into the hip  Hip socket  acetabulum  Closed over by bone on the inside o Dinosaurs eliminate this bone  Dinosaurs all have an open hip socket o Saurischia  Lizard hip is like all other reptiles o Ornithischia  Have an unusual hip  Opisthopuby  Rotate the pubis so that it is pointing backward  Also has another part of the pubis that juts forward  The muscles that are at the front of the animal come and attach to the pubis  The muscles are now moved way far back  Much more abdominal muscles are pushed farther back  Hadrosaurs  Have hollow crests  extensions of the nasal passage that have hypertrophied and been pulled back or looped on top of head  Pachycephalosaurs  Big chunk of solid bone on their head  Persistent hypothesis regarding behavior is that they were head-butters  An engineering study on the skull showed that the shape would withstand high stresses  Examination of the fossils shows the dome is made from very vascular bone o Lacks the material properties necessary to withstand head-butting stresses  Ceratopsians  Horned dinosaurs  Have a new bone at the front of their face  rostral bone  Grow “frills” of the back of their head  Hundred of skeletons are known o Theropoda and Sauropods  Formed the Saurischia  Sauropods  Late Triassic through Late Cretaceous  Largest land animals to ever evolve  Flat footprints o Fatty cushion at the back part of their feet o Very similar to elephant feet  Theropoda  Late Triassic – recent  Ostrich-mimics (Ornithomimids) o They were toothless  Oviraptors  “egg thief” o Have very strange skulls and are also toothless o Stealing the eggs of Protoceratops  Found eggs and nests and oviraptors on those nests  Eggs were found with embryos inside  They were Oviraptor babies, not Protoceratops o Law two eggs at once o Medullary bone in a chicken  Put down when ovulation starts  Full of calcium  Getting ready to lay eggs o Lines of Arrested Growth  Dromaeosaurs o Velociraptors o One lineage became quite small  They had feathers o We now know that most theropods had feathers o Had wishbones at the front of their chests o Elongate hands and cocked wrist with unique adaptations of the wrist bones o Birds originate by the Late Jurassic  Become very diverse and numerous throughout the Cretaceous  Get smaller and smaller  Invade ecological spaces that no one has before

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Textbook: Introduction to the Theory of Computation
Edition: 3
Author: Michael Sipser
ISBN: 9781133187790

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Let = {0,1}. Let WWk = {ww| w and w is of length k}. a.