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Subrecursive Programming Systems - Complexity & Succinctness (Hardcover, 1994 ed.)
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Subrecursive Programming Systems - Complexity & Succinctness (Hardcover, 1994 ed.)
Series: Progress in Theoretical Computer Science
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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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