 9.3.1: For each input sequence and machine given, compute the correspondin...
 9.3.2: a. For the machine described in Exercise la, find all input sequenc...
 9.3.3: In Exercises 36, write the state table for the machine, and compute...
 9.3.4: In Exercises 36, write the state table for the machine, and compute...
 9.3.5: In Exercises 36, write the state table for the machine, and compute...
 9.3.6: In Exercises 36, write the state table for the machine, and compute...
 9.3.7: In Exercises 710, draw the state graph for the machine, and compute...
 9.3.8: In Exercises 710, draw the state graph for the machine, and compute...
 9.3.9: In Exercises 710, draw the state graph for the machine, and compute...
 9.3.10: In Exercises 710, draw the state graph for the machine, and compute...
 9.3.11: a. Construct a finitestate machine that complements each bit of th...
 9.3.12: a. Construct a finitestate machine that will compute x + 1 where x...
 9.3.13: a. Construct a finitestate machine that will compute the bitwise A...
 9.3.14: a. Construct a finitestate machine that will compute the bitwise O...
 9.3.15: a. Construct a delay machine having input and output alphabet 50, 1...
 9.3.16: a. Construct a finitestate machine that will compute the 2s comple...
 9.3.17: You are designing a Windowsbased, eventdriven program to handle c...
 9.3.18: Whenever a video disk is inserted into a DVR, the machine automatic...
 9.3.19: You have an account at First National Usury Trust (FNUT) and a card...
 9.3.20: An elevator in a threestory building services floors 1, 2, and 3. ...
 9.3.21: For Exercises 2124, determine whether the given machine recognizes ...
 9.3.22: For Exercises 2124, determine whether the given machine recognizes ...
 9.3.23: For Exercises 2124, determine whether the given machine recognizes ...
 9.3.24: For Exercises 2124, determine whether the given machine recognizes ...
 9.3.25: a. set of all strings containing an even number of 0s b. set of all...
 9.3.26: a. set of all strings ending with one or more 0s b. set of all stri...
 9.3.27: a. set of all strings containing exactly one 1 b. set of all string...
 9.3.28: a. set of all strings consisting entirely of any number (including ...
 9.3.29: A paragraph of English text is to be scanned and the number of word...
 9.3.30: a. In many computer languages, any decimal number N must be present...
 9.3.31: Let M be a finitestate machine with n states. The input alphabet i...
 9.3.32: At the beginning of the chapter, we learn: Your team at Babel, Inc....
 9.3.33: For Exercises 3338, give a regular expression for the set recognize...
 9.3.34: For Exercises 3338, give a regular expression for the set recognize...
 9.3.35: For Exercises 3338, give a regular expression for the set recognize...
 9.3.36: For Exercises 3338, give a regular expression for the set recognize...
 9.3.37: For Exercises 3338, give a regular expression for the set recognize...
 9.3.38: For Exercises 3338, give a regular expression for the set recognize...
 9.3.39: For Exercises 3942, give a regular expression for the set recognize...
 9.3.40: For Exercises 3942, give a regular expression for the set recognize...
 9.3.41: For Exercises 3942, give a regular expression for the set recognize...
 9.3.42: For Exercises 3942, give a regular expression for the set recognize...
 9.3.43: Give a regular expression for each of the following sets. a. set of...
 9.3.44: Give a regular expression for each of the following sets. a. set of...
 9.3.45: Does the given string belong to the given regular set? a. 01110111;...
 9.3.46: Does the given string belong to the given regular set? a. 1000011; ...
 9.3.47: Write a regular expression for the set of all arithmetic expression...
 9.3.48: Write a regular expression for the set of all alphanumeric strings ...
 9.3.49: Write regular expressions for each of the strings described in Exer...
 9.3.50: Write regular expressions for each of the strings described in Exer...
 9.3.51: Write regular expressions for each of the strings described in Exer...
 9.3.52: Write regular expressions for each of the strings described in Exer...
 9.3.53: a. Prove that if A is a regular set, then the set AR consisting of ...
 9.3.54: Prove that if A is a regular set whose symbols come from the alphab...
 9.3.55: For Exercises 5562, decide which of the given strings match the giv...
 9.3.56: For Exercises 5562, decide which of the given strings match the giv...
 9.3.57: For Exercises 5562, decide which of the given strings match the giv...
 9.3.58: For Exercises 5562, decide which of the given strings match the giv...
 9.3.59: For Exercises 5562, decide which of the given strings match the giv...
 9.3.60: For Exercises 5562, decide which of the given strings match the giv...
 9.3.61: For Exercises 5562, decide which of the given strings match the giv...
 9.3.62: For Exercises 5562, decide which of the given strings match the giv...
 9.3.63: Identify any unreachable states of M. Present state Next state Output
 9.3.64: Identify any unreachable states of M. Present state Next state Output
 9.3.65: For Exercises 6574, minimize the given machine.
 9.3.66: For Exercises 6574, minimize the given machine.
 9.3.67: For Exercises 6574, minimize the given machine.
 9.3.68: For Exercises 6574, minimize the given machine.
 9.3.69: For Exercises 6574, minimize the given machine.
 9.3.70: For Exercises 6574, minimize the given machine.
 9.3.71: For Exercises 6574, minimize the given machine.
 9.3.72: For Exercises 6574, minimize the given machine.
 9.3.73: For Exercises 6574, minimize the given machine.
 9.3.74: For Exercises 6574, minimize the given machine.
 9.3.75: Construct a sequential network for the finitestate machine of Exer...
 9.3.76: Construct a sequential network for the finitestate machine of Exer...
Solutions for Chapter 9.3: FiniteState Machines
Full solutions for Mathematical Structures for Computer Science  7th Edition
ISBN: 9781429215107
Solutions for Chapter 9.3: FiniteState Machines
Get Full SolutionsMathematical Structures for Computer Science was written by Patricia and is associated to the ISBN: 9781429215107. Chapter 9.3: FiniteState Machines includes 76 full stepbystep solutions. Since 76 problems in chapter 9.3: FiniteState Machines have been answered, more than 5369 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: Mathematical Structures for Computer Science, edition: 7.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.
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