 1.1.1: The followingare the state diagrams of two DFAs, M1 and M2. Answer ...
 1.1.2: Give the formal description of the machines M1 and M2 pictured in E...
 1.1.3: The formal description of a DFA M is {q1,q2,q3,q4,q5},{u,d},,q3,{q3...
 1.1.4: Each of the following languages is the intersection of two simpler ...
 1.1.5: Each of the following languages is the complement of a simpler lang...
 1.1.6: Give state diagrams of DFAs recognizing the following languages. In...
 1.1.7: Give state diagrams of NFAs with the specied number of states recog...
 1.1.8: Use the construction in the proof of Theorem 1.45 to give the state...
 1.1.9: Use the construction in the proof of Theorem 1.47 to give the state...
 1.1.10: Use the construction in the proof of Theorem 1.49 to give the state...
 1.1.11: Prove that everyNFA can be converted to an equivalentone that has a...
 1.1.12: Let D = {w w contains an even number of as and an odd number of bs...
 1.1.13: Let F be the language of all strings over {0,1} that do not contain...
 1.1.14: a. Show that if M is a DFA that recognizes language B, swapping the...
 1.1.15: Give a counterexample to show that the following construction fails...
 1.1.16: Use the construction given in Theorem 1.39 to convert the following...
 1.1.17: a. Give an NFA recognizing the language (01 001 010). b. Convert th...
 1.1.18: Give regular expressions generating the languages of Exercise 1.6.
 1.1.19: Use the procedure described in Lemma 1.55 to convert the following ...
 1.1.20: For each of the following languages, give two strings that are memb...
 1.1.21: Use the procedure described in Lemma 1.60 to convert the following ...
 1.1.22: In certain programming languages, comments appear between delimiter...
 1.1.23: Let B be any language over the alphabet . Prove that B = B+ iff BB B.
 1.1.24: A nite state transducer (FST) is a type of deterministic nite autom...
 1.1.25: Read the informal denition of the nite state transducer given in Ex...
 1.1.26: Using the solution you gave to Exercise 1.25, give a formal descrip...
 1.1.27: Read the informal denition of the nite state transducer given in Ex...
 1.1.28: Convert the following regular expressions to NFAs using the procedu...
 1.1.29: Use the pumping lemma to show that the following languages are not ...
 1.1.30: Describe theerror in thefollowingproof that 01 is not a regular lan...
 1.1.31: For any string w = w1w2 wn, the reverse of w, written wR, is the st...
 1.1.32: Let 3 =nh0 0 0i,h0 0 1i,h0 1 0i,...,h1 1 1io. 3 contains all size 3...
 1.1.33: Let2 =0 0,0 1,1 0,1 1.Here, 2 contains all columns of 0s and 1s of ...
 1.1.34: Let 2 be the same as in 1.33. Consider each row to be a binary numb...
 1.1.35: 01 01 10 0 D, but0 00 11 10 06 D. Show that D is regular.1.35 Let 2...
 1.1.36: 01 01 10 0 D, but0 00 11 10 06 D. Show that D is regular.1.35 Let 2...
 1.1.37: Let Cn = {x x is a binary number that is a multiple of n}. Show th...
 1.1.38: An allNFA M is a 5tuple (Q,,,q0,F) that accepts x if every possib...
 1.1.39: TheconstructioninTheorem1.54showsthateveryGNFAisequivalenttoaGNFA w...
 1.1.40: Recall that string x is a prex of string y if a string z exists whe...
 1.1.41: For languages A and B, let the perfect shufe of A and B be the lang...
 1.1.42: For languages A and B, let the shufe of A and B be the language {w...
 1.1.43: Let A be any language. Dene DROPOUT(A) to be the language containi...
 1.1.44: Let B and C be languages over = {0,1}. DeneB1 C = {wB for some yC,...
 1.1.45: Let A/B = {w wx A for some x B}. Show that if A is regular and B i...
 1.1.46: Prove that the following languages are not regular. You may use the...
 1.1.47: Let = {1,#} and letY = {w w = x1#x2##xk for k 0, each xi 1, and xi...
 1.1.48: Let = {0,1} and letD = {ww contains an equal number of occurrences...
 1.1.49: a. Let B = {1ky y {0,1} and y contains at least k 1s, for k 1}. Sh...
 1.1.50: Read the informal denition of the nite state transducer given in Ex...
 1.1.51: Let x and y be strings and let L be any language. We say that x and...
 1.1.52: MyhillNerode theorem. Refer to 1.51. Let L be a language and let X ...
 1.1.53: Let = {0,1,+,=} andADD = {x=y+z x,y,z are binary integers, and x i...
 1.1.54: Consider the language F = {aibjck i,j,k 0 and if i = 1 then j = k}...
 1.1.55: Thepumping lemma says thatevery regular languagehas a pumping lengt...
 1.1.56: If A is a set of natural numbers and k is a natural number greater ...
 1.1.57: If A is any language, let A1 2 be the set of all rst halves of stri...
 1.1.58: If A is any language, let A1 3 1 3be the set of all strings in A wi...
 1.1.59: Let M = (Q,,,q0,F) be a DFA and let h be a state of M called its ho...
 1.1.60: Let = {a,b}. For each k 1, let Ck be the language consisting of all...
 1.1.61: Consider the languages Ck dened in 1.60. Prove that for each k, no ...
 1.1.62: Let = {a,b}. For each k 1, let Dk be the language consisting of all...
 1.1.63: a. Let A be an innite regular language. Prove that A can be split i...
 1.1.64: Let N be an NFA with k states that recognizes some language A.a. Sh...
 1.1.65: Prove that for each n > 0, a language Bn exists where a. Bn is reco...
 1.1.66: A homomorphism is a function f : from one alphabet to strings over ...
 1.1.67: Let the rotational closure of language A be RC(A) = {yx xy A}. a. ...
 1.1.68: In the traditional method for cutting a deck of playing cards, the ...
 1.1.69: Let = {0,1}. Let WWk = {ww w and w is of length k}. a. Show that f...
 1.1.70: We dene the avoids operation for languages A and B to beA avoids B ...
 1.1.71: Let = {0,1}. a. Let A = {0ku0k k 1 and u }. Show that A is regular...
 1.1.72: Let M1 and M2 be DFAs that have k1 and k2 states, respectively, and...
 1.1.73: Let = {0,1,#}. Let C = {x#xR#x x {0,1}}. Show that C is a CFL.
Solutions for Chapter 1: R E G U L A R L A N G U A G E S
Full solutions for Introduction to the Theory of Computation  3rd Edition
ISBN: 9781133187790
Solutions for Chapter 1: R E G U L A R L A N G U A G E S
Get Full SolutionsThis textbook survival guide was created for the textbook: Introduction to the Theory of Computation, edition: 3. Chapter 1: R E G U L A R L A N G U A G E S includes 73 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 73 problems in chapter 1: R E G U L A R L A N G U A G E S have been answered, more than 18695 students have viewed full stepbystep solutions from this chapter. Introduction to the Theory of Computation was written by and is associated to the ISBN: 9781133187790.

Absolute magnitude
The apparent brightness of a star if it were viewed from a distance of 10 parsecs (32.6 lightyears). Used to compare the true brightness of stars.

Annual temperature range
The difference between the highest and lowest monthly temperature means.

Bathymetry
The measurement of ocean depths and the charting of the shape or topography of the ocean floor.

Bed load
Sediment that is carried by a stream along the bottom of its channel.

Body waves
Seismic waves that travel through Earth’s interior.

Breccia
A sedimentary rock composed of angular fragments that were lithified.

Crater
The depression at the summit of a volcano, or that which is produced by a meteorite impact.

Environmental lapse rate
The rate of temperature decrease with increasing height in the troposphere.

Fossil magnetism
See Paleomagnetism.

Glaze
A coating of ice on objects formed when supercooled rain freezes on contact.

Hogback
A narrow, sharpcrested ridge formed by the upturned edge of a steeply dipping bed of resistant rock.

Kuiper belt
A region outside the orbit of Neptune where most shortperiod comets are thought to originate.

Melt
The liquid portion of magma, excluding the solid crystals.

Meteor
The luminous phenomenon observed when a meteoroid enters Earth’s atmosphere and burns up; popularly called a “shooting star.”

Parent material
The material upon which a soil develops.

Primary productivity
The amount of organic matter synthesized by organisms from inorganic substances through photosynthesis or chemosynthesis within a given volume of water or habitat in a unit of time.

Striations (glacial)
Scratches or grooves in a bedrock surface caused by the grinding action of a glacier and its load of sediment.

Surface waves
Seismic waves that travel along the outer layer of Earth.

Tropical rain forest
A luxuriant broadleaf evergreen forest; also, the name given the climate associated with this vegetation.

Volatiles
Gaseous components of magma dissolved in the melt. Volatiles will readily vaporize (form a gas) at surface pressures.