Prof. Borut Robič received his Ph.D. in Computer Science from the University of Ljubljana in 1993. He is a member of the Faculty of Computer and Information Science of the University of Ljubljana where he leads the Laboratory for Algorithms and Data Structures. He has had guest professorships, fellowships and collaborations with the University of Cambridge, the University of Augsburg, the University of Grenoble, and the Jožef Stefan Institute in Ljubljana. His research interests and teaching experience address algorithms; computability and computational complexity theory; parallel, distributed and grid computing; operating systems; and processor architectures. In addition to the 1st ed. of the current book, Prof. Robič coauthored the books "Processor Architecture: From Dataflow to Superscalar and Beyond" (Springer 1999) and "Introduction to Parallel Computing: From Algorithms to Programming on State-of-the-Art Platforms" (Springer 2018).

• Part I, The Roots of Computability Theory.- Introduction.- The Foundational Crisis of Mathematics.- Formalism.- Hilbert’s Attempt at Recovery.- Part II, Classicial Computability Theory.- The Quest for a Formalization.- The Turing Machine.- The First Basic Results.- Incomputable Problems.- Methods of Proving Incomputability.- Part III, Relative Computability.- Computation with External Help.- Degrees of Unsolvability.- The Turing Hierarchy of Unsolvability.- The Class D of Degrees of Unsolvability.- C.E. Degrees and the Priority Method.- The Arithmetical Hierarchy.- Part IV, Back to the Roots.- Computability (Church-Turing) Thesis Revisited.- Further Reading.- App. A, Mathematical Background.- App. B, Notation Index.- Glossary.- References.- Index.

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Prof. Borut Robič received his Ph.D. in Computer Science from the University of Ljubljana in 1993. He is a member of the Faculty of Computer and Information Science of the University of Ljubljana where he leads the Laboratory for Algorithms and Data Structures. He has had guest professorships, fellowships and collaborations with the University of Cambridge, the University of Augsburg, the University of Grenoble, and the Jožef Stefan Institute in Ljubljana. His research interests and teaching experience address algorithms; computability and computational complexity theory; parallel, distributed and grid computing; operating systems; and processor architectures. In addition to the 1st ed. of the current book, Prof. Robič coauthored the books "Processor Architecture: From Dataflow to Superscalar and Beyond" (Springer 1999) and "Introduction to Parallel Computing: From Algorithms to Programming on State-of-the-Art Platforms" (Springer 2018).

• Part I, The Roots of Computability Theory.- Introduction.- The Foundational Crisis of Mathematics.- Formalism.- Hilbert’s Attempt at Recovery.- Part II, Classicial Computability Theory.- The Quest for a Formalization.- The Turing Machine.- The First Basic Results.- Incomputable Problems.- Methods of Proving Incomputability.- Part III, Relative Computability.- Computation with External Help.- Degrees of Unsolvability.- The Turing Hierarchy of Unsolvability.- The Class D of Degrees of Unsolvability.- C.E. Degrees and the Priority Method.- The Arithmetical Hierarchy.- Part IV, Back to the Roots.- Computability (Church-Turing) Thesis Revisited.- Further Reading.- App. A, Mathematical Background.- App. B, Notation Index.- Glossary.- References.- Index.

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Prof. Borut Robič received his Ph.D. in Computer Science from the University of Ljubljana in 1993. He is a member of the Faculty of Computer and Information Science of the University of Ljubljana where he leads the Laboratory for Algorithms and Data Structures. He has had guest professorships, fellowships and collaborations with the University of Cambridge, the University of Augsburg, the University of Grenoble, and the Jožef Stefan Institute in Ljubljana. His research interests and teaching experience address algorithms; computability and computational complexity theory; parallel, distributed and grid computing; operating systems; and processor architectures. In addition to the 1st ed. of the current book, Prof. Robič coauthored the books "Processor Architecture: From Dataflow to Superscalar and Beyond" (Springer 1999) and "Introduction to Parallel Computing: From Algorithms to Programming on State-of-the-Art Platforms" (Springer 2018).

• Part I, The Roots of Computability Theory.- Introduction.- The Foundational Crisis of Mathematics.- Formalism.- Hilbert’s Attempt at Recovery.- Part II, Classicial Computability Theory.- The Quest for a Formalization.- The Turing Machine.- The First Basic Results.- Incomputable Problems.- Methods of Proving Incomputability.- Part III, Relative Computability.- Computation with External Help.- Degrees of Unsolvability.- The Turing Hierarchy of Unsolvability.- The Class D of Degrees of Unsolvability.- C.E. Degrees and the Priority Method.- The Arithmetical Hierarchy.- Part IV, Back to the Roots.- Computability (Church-Turing) Thesis Revisited.- Further Reading.- App. A, Mathematical Background.- App. B, Notation Index.- Glossary.- References.- Index.

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