 2.2.1: Recall the CFG G4 that we gave in Example 2.4. For convenience, let...
 2.2.2: a. Use the languages A = {ambncnm,n 0} and B = {anbncmm,n 0} toge...
 2.2.3: Answer each part for the following contextfree grammar G.R XRX  S...
 2.2.4: Give contextfree grammars that generate the followinglanguages. In...
 2.2.5: Give informal descriptions and state diagrams of pushdown automata ...
 2.2.6: Give contextfree grammars generating the following languages. Aa. ...
 2.2.7: Give informal English descriptions of PDAs for the languages in Exe...
 2.2.8: Show that the string the girl touches the boy with the flower has t...
 2.2.9: Give a contextfree grammar that generates the languageA = {aibjck...
 2.2.10: Give an informal description of a pushdown automaton that recognize...
 2.2.11: Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, usin...
 2.2.12: ConverttheCFGGgiveninExercise2.3toanequivalentPDA,usingtheprocedure...
 2.2.13: Let G = (V,,R,S) be the following grammar. V = {S,T,U}; = {0,#}; an...
 2.2.14: Convert the following CFG into an equivalent CFG in Chomsky normal ...
 2.2.15: Give a counterexample to show that the following construction fails...
 2.2.16: Showthattheclassofcontextfreelanguagesisclosedundertheregularopera...
 2.2.17: Use the resultsof Exercise 2.16 to give another proof that every re...
 2.2.18: a. Let C be a contextfree language and R be a regular language. Pr...
 2.2.19: Let CFG G be the following grammar.S aSb  bY  Y a Y bY  aY  Giv...
 2.2.20: Let A/B = {w wx A for some x B}. Show that if A is context free an...
 2.2.21: Let = {a,b}. Give a CFG generating the language of strings with twi...
 2.2.22: Let C = {x#y x,y {0,1} and x 6= y}. Show that C is a contextfree ...
 2.2.23: LetD = {xyx,y {0,1} andx = ybutx 6= y}. ShowthatD isa context...
 2.2.24: Let E = {aibj i 6= j and 2i 6= j}. Show that E is a contextfree l...
 2.2.25: For any language A, let SUFFIX(A) = {v uv A for some string u}. Sh...
 2.2.26: Show that if G is a CFG in Chomsky normal form, then for any string...
 2.2.27: Let G = (V,,R,hSTMTi) be the following grammar.hSTMTi hASSIGNi  hI...
 2.2.28: Give unambiguous CFGs for the following languages.a. {w in every p...
 2.2.29: Show that the language A in Exercise 2.9 is inherently ambiguous.
 2.2.30: Use the pumping lemma to show that the followinglanguages are not c...
 2.2.31: Let B be the language of all palindromes over {0,1} containing equa...
 2.2.32: Let = {1,2,3,4} and C = {w  in w, the number of 1s equals the numb...
 2.2.33: Show that F = {aibj i = kj for some positive integer k} is not con...
 2.2.34: Consider the language B = L(G), where G is the grammar given in Exe...
 2.2.35: Let G be a CFG in Chomsky normal form that contains b variables. Sh...
 2.2.36: Give an example of a language that is not context free but that act...
 2.2.37: Prove the following stronger form of the pumping lemma, wherein bot...
 2.2.38: Referto 1.41 for thedenitionof the perfectshufeoperation. Showthat ...
 2.2.39: Refer to 1.42 for the denition of the shufe operation. Show that th...
 2.2.40: Say that a language is prexclosed if all prexes of every string in...
 2.2.41: Read the denitions of NOPREFIX(A) and NOEXTEND(A) in 1.40. a. Show ...
 2.2.42: Let Y ={w w=t1#t2##tk for k0, each ti 1, and ti 6=tj whenever i6=j...
 2.2.43: For strings w and t, write w $ t if the symbols of w are a permutat...
 2.2.44: If A and B are languages, dene A B = {xy x A and y B and x = y...
 2.2.45: Let A = {wtwR w,t {0,1} and w = t}. Prove that A is not a CFL.
 2.2.46: Consider the following CFG G:S SS  T T aTb  abDescribe L(G) and s...
 2.2.47: Let = {0,1} and let B be the collection of strings that contain at ...
 2.2.48: Let = {0,1}. Let C1 be the language of all strings that contain a 1...
 2.2.49: We dened the rotational closure of language A to be RC(A) = {yx xy...
 2.2.50: We dened the CUT of language A to be CUT(A) = {yxz xyz A}. Show th...
 2.2.51: Show that every DCFG is an unambiguous CFG.
 2.2.52: Show that every DCFG generates a prexfree language.
 2.2.53: Show that the class of DCFLs is not closed under the following oper...
 2.2.54: Let G be the following grammar:S Ta a a T TaTb  TbTa  a. Show tha...
 2.2.55: Let G1 be the following grammar that we introduced in Example 2.45....
 2.2.56: Let A = L(G1) where G1 is dened in 2.55. Show that A is not a DCFL....
 2.2.57: Let B = {aibjck i,j,k 0 and i = j or i = k}. Prove that B is not a...
 2.2.58: Let C = {wwR w {0,1}}. Prove that C is not a DCFL. (Hint: Suppose ...
 2.2.59: If we disallow rules in CFGs, we can simplify the DKtest. In the ...
Solutions for Chapter 2: C O N T E X T  F R E E 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 2: C O N T E X T  F R E E L A N G U A G E S
Get Full SolutionsChapter 2: C O N T E X T  F R E E L A N G U A G E S includes 59 full stepbystep solutions. Since 59 problems in chapter 2: C O N T E X T  F R E E L A N G U A G E S have been answered, more than 17364 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to the Theory of Computation, edition: 3. Introduction to the Theory of Computation was written by and is associated to the ISBN: 9781133187790.

Bar
Common term for sand and gravel deposits in a stream channel.

Cosmology
The study of the universe.

Flare
A sudden brightening of an area on the Sun.

Hadean eon
A term found on some versions of the geologic time scale. It refers to the earliest interval (eon) of Earth history, and ended 4 billion years ago.

Hail
Nearly spherical ice pellets having concentric layers and formed by the successive freezing of layers of water.

HertzsprungRussell diagram
See HR diagram.

Igneous rock
A rock formed by the crystallization of molten magma.

Lunar eclipse
An eclipse of the Moon.

Marine west coast climate
A climate found on windward coasts from latitudes 40–65 degrees and dominated by maritime air masses. Winters are mild and summers are cool

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

Nonconformity
An unconformity in which older metamorphic or intrusive igneous rocks are overlain by younger sedimentary strata.

Occluded front
A front formed when a cold front overtakes a warm front. It marks the beginning of the end of a middlelatitude cyclone.

Saltation
Transportation of sediment through a series of leaps or bounces.

Sill
A tabular igneous body that was intruded parallel to the layering of preexisting rock.

Storm surge
The abnormal rise of the sea along a shore as a result of strong winds.

Surface soil
The uppermost layer in a soil profile: the A horizon.

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

Terrestrial planets
Any of the Earthlike planets, including Mercury, Venus, Mars, and Earth.

Thermosphere
The region of the atmosphere immediately above the mesosphere and characterized by increasing temperatures due to absorption of very shortwave solar energy by oxygen.

Vent
The surface opening of a conduit or pipe.