P=PSPACE Theorem: Does Anyone Know It?

Thread starter Dragonfall
Start date Oct 17, 2009
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In summary, The P=PSPACE Theorem, also known as the Savitch's Theorem, states that the complexity class P is equal to the complexity class PSPACE. It was first proved by Walter Savitch in 1970 and has significant implications in understanding the relationship between time and space complexity. The theorem has been extensively studied and applied in various fields of computer science and has been accepted as a fundamental concept. Some examples of problems that fall under the P=PSPACE complexity class include the Traveling Salesperson Problem, Boolean Satisfiability Problem, and the Game of Life.

Oct 17, 2009

Dragonfall

There's a theorem which says if one class equals another class, then P=PSPACE. Does anyone know what it is?

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Oct 20, 2009

Dragonfall

Anyone?

1. What is the P=PSPACE Theorem?

The P=PSPACE Theorem, also known as the Savitch's Theorem, is a mathematical proof that states that the complexity class P (problems that can be solved in polynomial time) is equal to the complexity class PSPACE (problems that can be solved using polynomial space). In simpler terms, it means that any problem that can be solved efficiently can also be solved using a limited amount of memory.

2. Who came up with the P=PSPACE Theorem?

The P=PSPACE Theorem was first proved by Walter Savitch in 1970. However, the concept was first introduced by Juris Hartmanis and Richard E. Stearns in their paper "On the Computational Complexity of Algorithms" published in 1965.

3. How does the P=PSPACE Theorem impact computer science?

The P=PSPACE Theorem has a significant impact on computer science as it helps in understanding the relationship between time and space complexity. It also provides insights into the limitations of computers and helps in the development of efficient algorithms and data structures for solving complex problems.

4. Is the P=PSPACE Theorem proven to be true?

Yes, the P=PSPACE Theorem has been proven to be true through mathematical proofs and has been accepted as a fundamental concept in computer science. It has been extensively studied and applied in various fields, including complexity theory, artificial intelligence, and programming languages.

5. What are some examples of problems that fall under the P=PSPACE complexity class?

Some examples of problems that fall under the P=PSPACE complexity class include the Traveling Salesperson Problem, Boolean Satisfiability Problem, and the Game of Life. These are problems that can be solved efficiently and with limited memory, making them an essential part of computer science research and development.