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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT) 18.404J Theory of Computation (MIT)

Description

A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems. A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Subjects

computability | computability | computational complexity theory | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | Decidable and undecidable problems | reducibility | reducibility | recursive function theory | recursive function theory | Time and space measures on computation | Time and space measures on computation | completeness | completeness | hierarchy theorems | hierarchy theorems | inherently complex problems | inherently complex problems | oracles | oracles | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 18.404 | 18.404 | 6.840 | 6.840

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT) 18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory. This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Computability | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | computability | complexity | mathematical models | computation | finite representation | infinite objects | finite automata | regular languages | context-free languages | Turing machines | partial recursive functions | Church's Thesis | undecidability | reducibility | completeness | time complexity | NP-completeness | probabilistic computation | interactive proof systems | 6.045 | 18.400

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT)

Description

A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Subjects

computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | interactive proof systems | 18.404 | 6.840

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | computability | complexity | mathematical models | computation | finite representation | infinite objects | finite automata | regular languages | context-free languages | Turing machines | partial recursive functions | Church's Thesis | undecidability | reducibility | completeness | time complexity | NP-completeness | probabilistic computation | interactive proof systems | 6.045 | 18.400

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.404J Theory of Computation (MIT)

Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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