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Subrecursive Programming Systems: Complexity & Succinctness by James S. Royer

Subrecursive Programming Systems: Complexity & Succinctness

by James S. Royer
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Book cover type: Paperback
  • ISBN13: 9781461266808
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 253
  • Original Price: EUR 99.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 403 grams
  • BISAC Subject(s): Software Development & Engineering / General and Programming / General

1.1. What This Book is About This book is a study of - subrecursive programming systems, - efficiency/program-size trade-offs between such systems, and - how these systems can serve as tools in complexity theory. Section 1.1 states our basic themes, and Sections 1.2 and 1.3 give a general outline of the book. Our first task is to explain what subrecursive programming systems are and why they are of interest. 1.1.1. Subrecursive Programming Systems A subrecursive programming system is, roughly, a programming language for which the result of running any given program on any given input can be completely determined algorithmically. Typical examples are: 1. the Meyer-Ritchie LOOP language [MR67, DW83], a restricted assem- bly language with bounded loops as the only allowed deviation from straight-line programming; 2. multi-tape 'lUring Machines each explicitly clocked to halt within a time bound given by some polynomial in the length ofthe input (see [BH79, HB79]); 3. the set of seemingly unrestricted programs for which one can prove 1 termination on all inputs (see [Kre51, Kre58, Ros84]); and 4. finite state and pushdown automata from formal language theory (see [HU79]). lOr, more precisely, the collection of programs, p, ofsome particular general-purpose programming language (e.g., Lisp or Modula-2) for which there is a proof in some par- ticular formal system (e.g., Peano Arithmetic) that p halts on all inputs.

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