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OverviewThis book is based on notes for a master’s course given at Queen Mary, University of London, in the 1998/9 session. Such courses in London are quite short, and the course consisted essentially of the material in the ?rst three chapters, together with a two-hour lecture on connections with group theory. Chapter 5 is a considerably expanded version of this. For the course, the main sources were the books by Hopcroft and Ullman ([20]), by Cohen ([4]), and by Epstein et al. ([7]). Some use was also made of a later book by Hopcroft and Ullman ([21]). The ulterior motive in the ?rst three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Three such notions are considered. These are: generated by a type 0 grammar, recognised by a Turing machine (deterministic or not) and de?ned by means of a Godel ¨ numbering, having de?ned “recursively enumerable” for sets of natural numbers. It is hoped that this has been achieved without too many ar- ments using complicated notation. This is a problem with the entire subject, and it is important to understand the idea of the proof, which is often quite simple. Two particular places that are heavy going are the proof at the end of Chapter 1 that a language recognised by a Turing machine is type 0, and the proof in Chapter 2 that a Turing machine computable function is partial recursive. Full Product DetailsAuthor: Ian M. Chiswell , Sheldon Axler , Vincenzo Capasso , Carles CasacubertaPublisher: Springer London Ltd Imprint: Springer London Ltd Edition: 2009 ed. Dimensions: Width: 15.50cm , Height: 0.90cm , Length: 23.50cm Weight: 0.454kg ISBN: 9781848009394ISBN 10: 1848009399 Pages: 157 Publication Date: 06 February 2009 Audience: College/higher education , Postgraduate, Research & Scholarly , Undergraduate Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- Contents.- 1. Grammars and Machine Recognition.- 2. Recursive Functions.- 3. Recursively Enumerable Sets and Languages.- 4. Context-free language.- 5. Connections with Group Theory.- A. Results and Proofs Omitted in the Text.- B. The Halting Problem and Universal Turing Machines.- C. Cantor's Diagonal Argument.- D. Solutions to Selected Exercises.- References.- Index.ReviewsFrom the reviews: This short work by Chiswell ! covers formal languages, automata theory, and the word problem in group theory. This content is bound together by the unifying theme of what is known as Church's thesis, which states that any desirable definition of computability should coincide with recursiveness. ! Several appendixes serve as homes for ! distracting proofs of results needed in the main body of the text, or for solutions to selected instances of the abundant exercises. Summing Up: Recommended. Academic readers, upper-division undergraduates through researchers/faculty. (F. E. J. Linton, Choice, Vol. 46 (11), 2009) From the reviews: This short work by Chiswell ... covers formal languages, automata theory, and the word problem in group theory. This content is bound together by the unifying theme of what is known as Church's thesis, which states that any desirable definition of computability should coincide with recursiveness. ... Several appendixes serve as homes for ... distracting proofs of results needed in the main body of the text, or for solutions to selected instances of the abundant exercises. Summing Up: Recommended. Academic readers, upper-division undergraduates through researchers/faculty. (F. E. J. Linton, Choice, Vol. 46 (11), 2009) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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