theory of computation introduction - eg.bucknell.educsci341/2014-fall/notes/history.pdf · theory...

Mathematics & Logic Computer Science CSCI 341

Theory of ComputationIntroduction

CSCI 341 - Bucknell University

Fall 2013

Mathematics & Logic Computer Science CSCI 341

David Hilbert (1862-1943)

In 1900, Hilbert challenged the community of mathematicians with23 problems.

Mathematics & Logic Computer Science CSCI 341

Hilbert’s program

Secure the foundations of mathematics.

• Description of the language of Mathematics (Formal logic)

• Completeness (all true statements should be provable)

• Consistency (no contradiction should be found)

• Decidability (automatically prove theorems)

Mathematics & Logic Computer Science CSCI 341

Hilbert’s program

Secure the foundations of mathematics.

• Description of the language of Mathematics (Formal logic)

• Completeness (all true statements should be provable)

• Consistency (no contradiction should be found)

• Decidability (automatically prove theorems)

Mathematics & Logic Computer Science CSCI 341

Hilbert’s program

Secure the foundations of mathematics.

• Description of the language of Mathematics (Formal logic)

• Completeness (all true statements should be provable)

• Consistency (no contradiction should be found)

• Decidability (automatically prove theorems)

Mathematics & Logic Computer Science CSCI 341

Hilbert’s program

Secure the foundations of mathematics.

• Description of the language of Mathematics (Formal logic)

• Completeness (all true statements should be provable)

• Consistency (no contradiction should be found)

• Decidability (automatically prove theorems)

Mathematics & Logic Computer Science CSCI 341

Hilbert’s program

Secure the foundations of mathematics.

• Description of the language of Mathematics (Formal logic)

• Completeness (all true statements should be provable)

• Consistency (no contradiction should be found)

• Decidability (automatically prove theorems)

Mathematics & Logic Computer Science CSCI 341

Bertrand Russell (1872-1970)

Provide the first formal logic for mathematics in PrincipiaMathematica(joint work with Whitehead in 1910).

Mathematics & Logic Computer Science CSCI 341

Principia Mathematical 1910

.

Mathematics & Logic Computer Science CSCI 341

Kurt Godel (1906-1978)

• Godel’s Incompleteness Theorem (1st):In an effective logic system, there are statements that cannotbe proved nor disproved.

• Godel’s Incompleteness Theorem (2nd):In an effective logic system, the consistency of the system isnot provable within the system.

Mathematics & Logic Computer Science CSCI 341

Kurt Godel (1906-1978)

• Godel’s Incompleteness Theorem (1st):In an effective logic system, there are statements that cannotbe proved nor disproved.

• Godel’s Incompleteness Theorem (2nd):In an effective logic system, the consistency of the system isnot provable within the system.

Mathematics & Logic Computer Science CSCI 341

Godel is a VIP(the pizzeria slide)

Mathematics & Logic Computer Science CSCI 341

Alan Turing (1912-1954)

Break the enigma code and a pioneer in designing computers.

Undecidability: There are problems that cannot be solvedautomatically.

Mathematics & Logic Computer Science CSCI 341

Breaking Enigma Code

Machine used by Germany for encrypting information during WW2.

Mathematics & Logic Computer Science CSCI 341

Kleene, Rabin & Scott

In the 1950’s, pioneers of the Theory of Automata (Regularexpressions).

Mathematics & Logic Computer Science CSCI 341

Chomsky & Schutzenberger

In the 1960’s, pioneers in the study of Formal Grammar.

Mathematics & Logic Computer Science CSCI 341

Understanding language

Mathematics & Logic Computer Science CSCI 341

Stephen Cook

State the P vs NP problem in the 1970’s.

Mathematics & Logic Computer Science CSCI 341

Reward

The Clay Mathematics Institute is offering a

US$1 million reward

to anyone who has a formal proof that P = NP or that P 6= NP.

There are already more than 70 different proofs listed onhttp://www.win.tue.nl/~gwoegi/P-versus-NP.htm

Mathematics & Logic Computer Science CSCI 341

Reward

The Clay Mathematics Institute is offering a

US$1 million reward

to anyone who has a formal proof that P = NP or that P 6= NP.

There are already more than 70 different proofs listed onhttp://www.win.tue.nl/~gwoegi/P-versus-NP.htm

Mathematics & Logic Computer Science CSCI 341

Reward

The Clay Mathematics Institute is offering a

US$1 million reward

to anyone who has a formal proof that P = NP or that P 6= NP.

There are already more than 90 different proofs listed onhttp://www.win.tue.nl/~gwoegi/P-versus-NP.htm

Mathematics & Logic Computer Science CSCI 341

Christos Papadimitriou

Major contributor of the Computational Complexity Theory.Author of your Textbook !

Mathematics & Logic Computer Science CSCI 341

The life of Russell in a Comic Book

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

CSCI 341Theory of Computation

What are you going to learn during this semester?

• History

• Foundations

• Models of compution

• Practice formal proofs

• Implement the theory (Project)

• Critical thinking on article

Mathematics & Logic Computer Science CSCI 341

See you on Friday !