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# Theoretical Computer Science

Theoretical computer science is a division of general computer science and mathematics which focuses on the abstract and mathematical aspects of computing. The field of theoretical computer science is interpreted broadly to include algorithms, data structures, computational complexity, distributed computing, parallel computing, and quantum computing. Work in this field is often distinguished by its emphasis on mathematical technique and formal proofs.

Formal algorithms have existed for many years. However, it was not until 1936 when Alan Turing, Alonzo Church and Stephan Kleene formalized the definition of an algorithm. These developments have led to the modern study of logic, computability and computer science as a whole. Now the filed is abuzz with talk of the future of quantum computing, the most exciting potential future path that modern computing might take. Turing, Church (credit: Princeton University, Institution of Mathematics) and Kleene (credit: Konrad Jacobs, Erlangen)

The most important fields of theoretical computer science, and accordingly, those most often taught and studied, are as follows:

• theory of computation, including automata, computability and computational complexity theories
• programming language theory
• compiler theory
• artificial intelligence

## BrainMass Categories within Theoretical Computer Science

### Wiping Storage Media

This short article is about the importance of wiping storage media.

### CISC Versus RISC Computer Architecture

Please help with the following: Discuss the differences, strengths, and weaknesses in CISC Architecture and RISC Architecture.

### Impact of Multimedia and Technology in Our Lives

How do you think multimedia is changing our lives? Where does it penetrates our daily living and is it a good or bad effect? What do you think will develop in the near and in the far future?

### Amdahl's Law

(a) Illustrate Amdahl's law in terms of speedup vs. sequential portion of program by showing the speedup for N = 8 processors when the sequential portion of the program grows from 1% to 25%. (b) ( Amdahl's law) With sequential execution occurring 15% of the time: (i) What is the maximum speedup with an infinite number of

### Theory of computation

Summarize the significance of the halting problem in the field of theoretical computer science.

### Write a Turing machine algorithm to perform a unary decrement.

Write a Turing machine algorithm to perform a unary decrement. Assume that the input number may be 0, in which case a single 0 should be output on the tape to signify that the operation results in a negative number. When writing Turing machine algorithm, include comments for each instruction or related group of instructions.

### Draw Turing machine configurations and find the output as asked in the questions below.

For questions 3 to 5, remember that a Turing machine starts in state 1, reading the leftmost nonblank cell. 1. Given the Turing machine instruction (1,1,0,2,L) and the configuration ... b 1 0 b ... (Tape read head is in state 1, and is over symbol 1 on the left) Draw the next configuration. 2. A Tur

### What are the differences between hardware and software? Which is more important of these?

Often there is a discussion on which comes first: Hardware or Software? Which is more important, or is it that both are equally important? Discuss.

### Using the given Turing-machine model, create a program for a Turing machine that computes the function f(n) = 2n + 3.

Consider the following Turing-machine model (which is used in one of the standard textbooks in recursion theory, a branch of mathematical logic: Recursively Enumerable Sets and Degrees, by Robert I. Soare, Springer-Verlag, New York, 1987): The Turing machine is equipped with the following: (i) a tape that is infinitely lon

### Logic: Turing Machines

Please see the attached file for the fully formatted problems. (a) We wish to design a Turing machine which, using monadic notation, inputs a pair (in, n) of positive integers in standard starting position (on an otherwise blank tape), and which halts scanning the rightmost of a string of in is on an otherwise blank tape. W

### Turing-recognizable language

Let A be a turing-recognizable language consisting of descriptions of Turing machines, {&#61665;M1&#61681;, &#61665;M2&#61681;,...}, where every Mi is a decider. Prove that some decidable language D is not decided by any decider Mi whose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

### Turing Machine Probabilities

Let B be a probabilistic polynomial time Turing machine and let C be a language where, for some fixed 0 < &#61646;1 < &#61646;2 < 1, a. w &#61647; C implies Pr [B accepts w] &#61603; &#61646;1, and b. w &#61646; C implies Pr [B accepts w] &#61619; &#61646;2. Show that C &#61646; BPP. HINT: Use Lemma 10.5 to help you

### Automata

Let &#61542; be a 3cnf-formula. An &#61625; assignment to the variables of &#61542; is one where each clause contains two literals with unequal truth values. In other words an &#61625; -assignment satisfies &#61542; without assigning three true literals in any clause. a. Show that the negation of any &#61625;-assignment to

### Automata and Computability: Example Problem

Recall that NPSAT is the class of languages that are recognized by nondeterministic polynomial time Turing machines with an oracle for the satisfiability problem. Show that NPSAT = 2P. See attached file for full problem description.

### Automata and Computability

Consider the problem of testing whether a Turing machine M on an input w ever attempts to move its head left when its head is on the left-most tape cell. Formulate this problem as a language and show that it is undecidable.

### Automata and Computability

Let A = (attached) R and S are regular expressions and L(R) &#61645; L(S) . Show that A is decidable.

### Automata and Computability

Show that the collection of Turing-recognizable languages is closed under the operations of a. union. b. concatenation. c. star. d. intersection

### Automata and Computability

A Turing machine with doubly infinite tape is similar to an ordinary Turing machine except that its tape is infinite to the left as well as to the right. The tape is initially filled with blanks except for the portion that contains the input. Computation is defined as usual except that the head never encounters an end to the t

### Give the transitions for a turing machine to accept the given language.

Give the transitions for a turing machine that accepts the language given below. L = {AnBnCn : n>=1} Where, An denotes a raised to the power n (a^n) Bn denotes b raised to the power n (b^n) Cn denotes c raised to the power n (c^n)

### What major features should a perfect programming language include?

I have noticed that there are many languages, is this because no one language has all the major elements needed to be a perfect programming Language? What major features should a perfect programming language include? I am trying to understand the concepts and struggling.

### Turing machine to compute the product of positive integers

Construct a turing machine to compute the product x*y of any two positive integers x and y. Assume that the inputs x and y are represented in unary and are separated by a single 0.

### Turing Machine: Sequences with equal number of 1s and 0s

Give the transition list for a turing machine that will determine whether for an input sequence w over symbol set {0,1}, n0(w) = n1(w). n0(w) and n1(w) respectively indicate the count of 0s and 1s in the word 'w'.

### Turing Machine for even palindromes

Construct a turing machine that accepts the language {ww^R : w <- {a,b}+}, where w^R denotes w superscripted R - reverse of w. For example, if w = abb then w^R = bba ww^R = abbbba

### Turing machine with input in unary notation

Devise a Turing machine with input given in unary notation (i.e., a string of n 1's denotes the integer n, and numbers are delimited by 0's) such that the machine produces the following output: 0 if x is divisible by 4 1 if x is congruent to 1 modulo 4 2 if x is congruent to 2 modulo 4 3 if x is congruent to 3 modulo