## Function-algebraic characterizations of log and polylog parallel time (1994)

Venue: | Computational Complexity |

Citations: | 14 - 4 self |

### BibTeX

@ARTICLE{Bloch94function-algebraiccharacterizations,

author = {Stephen Bloch},

title = {Function-algebraic characterizations of log and polylog parallel time},

journal = {Computational Complexity},

year = {1994},

volume = {4},

pages = {193--206}

}

### OpenURL

### Abstract

Abstract. The main results of this paper are recursion-theoretic characterizations of two parallel complexity classes: the functions computable by uniform bounded fan-in circuit families of log and polylog depth (or equivalently, the functions bitwise computable by alternating Turing machines in log and polylog time). The present characterizations avoid the complex base functions, function constructors, and a priori size or depth bounds typical of previous work on these classes. This simplicity is achieved by extending the \tiered recursion " techniques of Leivant and Bellantoni&Cook. Key words. Circuit complexity � subrecursion. Subject classi cations. 68Q15, 03D20, 94C99. 1.

### Citations

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(Show Context)
Citation Context ...o be computable by constantdepth, bounded fan-in circuits|and only one composition and one recursion scheme. Essential to these simpler characterizations is the notion (introduced in Leivant 1990 and =-=Bellantoni & Cook 1992-=-) of classifying the parameters of a function into \tiers" by how they are used in the computation. The classi cation depends on whether a parameter is used only for local, bitwise operations or is us... |

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Citation Context ...� primitive functions have mixed-case names. A function has polynomial growth if its length is bounded by a polynomial p(j~xj) in the lengths of its inputs. A function has quasipolynomial growth (see =-=Barrington 1992-=-) if its length is bounded by a function of the form 2 p(jj~xjj) ,s6 Stephen Bloch for polynomial p, or equivalently if the length of its length is bounded by a polynomial p(jj~xjj) in the lengths of ... |

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(Show Context)
Citation Context ...ions|so easy as to be computable by constantdepth, bounded fan-in circuits|and only one composition and one recursion scheme. Essential to these simpler characterizations is the notion (introduced in =-=Leivant 1990-=- and Bellantoni & Cook 1992) of classifying the parameters of a function into \tiers" by how they are used in the computation. The classi cation depends on whether a parameter is used only for local, ... |

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