On the space and time complexity of functions computable by simple programs

We study the space and time complexity of functions computable by simple loop-free programs operating on integers. In particular, we show that any function $f(x_1 , \cdots ,x_k )$ computable by a program using only comparison-based conditional forward branching instructions and the arithmetic operat...

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Bibliographic Details
Published inSIAM journal on computing Vol. 12; no. 4; pp. 708 - 716
Main Authors TAT-HUNG CHAN, IBARRA, O. H
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1983
Subjects
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer science
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
Variables
Mathematical function
Algorithm
Calculability
Computing complexity
Turing machine
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Summary:We study the space and time complexity of functions computable by simple loop-free programs operating on integers. In particular, we show that any function $f(x_1 , \cdots ,x_k )$ computable by a program using only comparison-based conditional forward branching instructions and the arithmetic operations $ + , - $, and truncating division by integer constants (such programs compute exactly the functions definable in Presburger arithmetic) can be computed by an off-line Turing machine in space $s(n)$ and time $n^2 /s(n)$ for any reasonable space bound $s(n)$ between $\log n$ and $n$. Moreover, the space-time trade-off is optimal.
ISSN:0097-5397
1095-7111
DOI:10.1137/0212048