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Questions and Answers
What does the P in the P class stand for?
What does the P in the P class stand for?
- Problem Complexity
- Polynomial Time (correct)
- Problem Solvability
- Practical Solutions
What type of problems are included in the P class?
What type of problems are included in the P class?
- Decision problems solvable in polynomial time (correct)
- Optimization problems with fast solutions
- Non-deterministic problems with efficient solutions
- Exponential time complexity problems
What does 'tractable' mean in the context of complexity classes?
What does 'tractable' mean in the context of complexity classes?
- Problems with unknown solutions
- Problems solvable in theory and practice (correct)
- Problems with exponential time complexity
- Problems solvable only in theory
What are problems called if they can be solved in theory but not in practice?
What are problems called if they can be solved in theory but not in practice?
What is the primary focus of complexity theory?
What is the primary focus of complexity theory?
What does Co-NP stand for?
What does Co-NP stand for?
If a problem X is in NP, what can be said about its complement X'?
If a problem X is in NP, what can be said about its complement X'?
What is a characteristic of NP-hard problems?
What is a characteristic of NP-hard problems?
What is the relationship between NP and CoNP problems in terms of verification?
What is the relationship between NP and CoNP problems in terms of verification?
What is the defining property of NP-hard problems in relation to problems in NP?
What is the defining property of NP-hard problems in relation to problems in NP?
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Study Notes
Complexity Classes
- P class stands for "Polynomial Time" and includes decision problems that can be solved in polynomial time.
- Problems in the P class are "tractable" or have efficient algorithms, meaning they can be solved quickly.
NP and Co-NP Complexity Classes
- NP stands for "Nondeterministic Polynomial Time" and includes decision problems where a proposed solution can be verified in polynomial time.
- Co-NP is the complementary class of NP, containing decision problems where a proposed solution cannot be verified in polynomial time.
NP-hard and NP-complete Problems
- NP-hard problems are at least as hard as the hardest problems in NP, but are not necessarily in NP themselves.
- A characteristic of NP-hard problems is that they can be reduced to an NP-complete problem in polynomial time.
Verification of NP and Co-NP Problems
- For an NP problem, a proposed solution can be verified in polynomial time.
- Verification of Co-NP problems is the complement of NP, meaning a proposed solution cannot be verified in polynomial time.
Complementary Problems
- If a problem X is in NP, its complement X' is in Co-NP.
Focus of Complexity Theory
- The primary focus of complexity theory is the classification of computational problems based on their difficulty.
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