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Full-Text Articles in Physical Sciences and Mathematics
Hierarchical Analysis Of A Distributed Evaluator, Robert M. Keller, Gary Lindstrom
Hierarchical Analysis Of A Distributed Evaluator, Robert M. Keller, Gary Lindstrom
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We outline the analysis of a distributed evaluator for an applicative language FGL (Function Graph Language). Our goal is to show that the least fixed point semantics of FGL are faithfully implemented by the hardware evaluator envisioned in the Applicative Multi-Processor System AMPS. Included in the analysis are a formalization of demand-driven computation , the introduction of an intermediate graphic language IGL to aid in our proofs, and discussion of pragmatic issues involved in the AMPS machine language design.
On The Evaluation Of Powers And Monomials, Nicholas Pippenger
On The Evaluation Of Powers And Monomials, Nicholas Pippenger
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Let $y_1 , \cdots ,y_p $ be monomials over the indeterminates $x_1 , \cdots ,x_q $. For every $y = (y_1 , \cdots ,y_p )$ there is some minimum number $L(y)$ of multiplications sufficient to compute $y_1 , \cdots ,y_p $ from $x_1 , \cdots ,x_q $ and the identity 1. Let $L(p,q,N)$ denote the maximum of $L(y)$ over all $y$ for which the exponent of any indeterminate in any monomial is at most $N$. We show that if $p = (N + 1^{o(q)} )$ and $q = (N + 1^{o(p)} )$, then $L(p,q,N) = \min \{ p,q\} \log N …
Comparative Schematology And Pebbling With Auxiliary Pushdowns, Nicholas J. Pippenger
Comparative Schematology And Pebbling With Auxiliary Pushdowns, Nicholas J. Pippenger
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This paper has three claims to interest. First, it combines comparative schematology with complexity theory. This combination is capable of distinguishing among Strong's “languages of maximal power,” a distinction not possible when comparative schematology is based on computability considerations alone, and it is capable of establishing exponential disparities in running times, a capability not currently possessed by complexity theory alone. Secondly, this paper inaugurates the study of pebbling with auxiliary pushdowns, which bears to plain pebbling the same relationship as Cook's study of space-bounded machines with auxiliary pushdowns bears to plain space-bounded machines. This extension of pebbling serves as the …