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SIAM Journal on Computing 1977年第3期6卷 427-443页

作者： Wolfgang J. Paul

Consider the combinational complexity L(f)L(f)L(f) of Boolean functions over the basis <span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" style="position: relative;&q... 详细信息

Consider the combinational complexity

L (f)

$L(f)$ of Boolean functions over the basis

关键词： combinational complexity circuit size

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PARALLEL PREFIX COMPUTATION

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JOURNAL OF THE ACM 1980年第4期27卷 831-838页

作者： LADNER, RE FISCHER, MJ Department of Computer Science FR-35 University of Washington Seattle Washington Department of Computer Science FR-35 University of Washington Seattle Washington

The prefix problem is to compute all the products x t o x2 o xk for iik in, where o is an associative operation A recurstve construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fast, small Boolean ctrcmts to simulate fimte-state transducers. By simulating a sequentml adder, a Boolean clrcmt which has depth 2[Iog2n] + 2 and size bounded by 14n Is obtained for n-bit binary addmon The size can be decreased significantly by permitting the depth to increase by an addmve constant. © 1980, ACM. All rights reserved.

关键词： automaton binary addmon clrcmt combinational complexity depth fanout parallehsm size transducer

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COMPLEX PROPERTIES OF GRAMMARS

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JOURNAL OF THE ACM 1980年第3期27卷 484-498页

作者： ABRAMSON, FG BREITBART, Y LEWIS, FD UNIV WISCONSIN MILWAUKEEWI 53201 UNIV KENTUCKY DEPT COMP SCILEXINGTONKY 40506

It is shown that several natural, undecidable properties of grammars are such that the size of the smallest Turing machine which correctly answers questions of length n grows at a nearly maximal rate as n grows. Thus, in a certain sense, even the finite initial segments of these properties are very complex. In fact, there are natural recursively enumerable properties of grammars such that if it is required that programs run in any fixed recursive time, then the same results hold. The present techniques also enable specific Boolean functionsfn to be exhibited, such that computingfn by a combinational circuit requires a number of gates exponential in the number of inputs to fn. © 1980, ACM. All rights reserved.

关键词： combinational complexity complex Boolean functions computational complexity context-free grammars formal grammars natural complex problems nonrecursive languages program-size complexity pushdown automata recursively enumerable sets reduction procedures time/size trade-offs undecidable properties

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