 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 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 17338 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.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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  ).

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.