Complexity theory exam

  • What is the complexity theory in math?

    Complexity theory is basically the study of what's hard or easy to solve with a computer.
    In it, the key thing is how the number of steps it takes to solve a problem grows with the size of the input..

  • What is the complexity theory in math?

    The theory of classifying problems based on how difficult they are to solve.
    A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to solve it is bounded by some power of the problem's size..

  • Complexity theory is a central topic in theoretical computer science.
    It has direct applications to computability theory and uses computation models such as Turing machines to help test complexity.
    Complexity theory helps computer scientists relate and group problems together into complexity classes.
  • Put succinctly, computability theory is concerned with what can be computed versus what cannot; complexity is concerned with the resources required to compute the things that are computable.
Past exam papers: Complexity Theory. Solution notes are available for many past questions to local users. They were produced by question setters, primarily for 

How do we define space complexity?

In defining space complexity, we assume machine M, which has a read-only input tape, and separate work tapes

We only count cells on the work tapes towards the complexity

Similarly, we define NSPACE(f(n)) to be the class of languages accepted by a nondeterministic machine which uses at most O(f(n)) tape cells on inputs of length n

What is a good book on computational complexity?

Introduction to the Theory of Computation, (First edition - PWS Publishing Company, January 1997, or second edition - Thomson Course Technology, 2005)

Arora, Barak Computational Complexity Cambridge University Press, 2009 I Wegener

Complexity Theory, Springer, 2005

C H Papadimitriou

What is complexity theory?

Complexity Theory Notes for a course of lectures for students of Part 1B of the Computer Science Tripos

Anuj Dawar University of Cambridge Computer Laboratory William Gates Building JJ Thomson Avenue Cambridge CB3 0FD

The aim of complexity theory is to understand what makes certain problems difficult to solve algorithmically

Appraisal theory is the theory in psychology that emotions are extracted from our evaluations of events that cause specific reactions in different people.
Essentially, our appraisal of a situation causes an emotional, or affective, response that is going to be based on that appraisal.
An example of this is going on a first date.
If the date is perceived as positive, one might feel happiness, joy, giddiness, excitement, and/or anticipation, because they have appraised this event as one that could have positive long-term effects, i.e. starting a new relationship, engagement, or even marriage.
On the other hand, if the date is perceived negatively, then our emotions, as a result, might include dejection, sadness, emptiness, or fear.
Reasoning and understanding of one's emotional reaction becomes important for future appraisals as well.
The important aspect of the appraisal theory is that it accounts for individual variability in emotional reactions to the same event.

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