8 Dec 2000 22:24:00 -0500

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Meaning of symbol in set theory? mikesw@whiterose.net (2000-12-06) |

Re: Meaning of symbol in set theory? offner@zko.dec.com (Carl Offner) (2000-12-07) |

Re: Meaning of symbol in set theory? soenke.kannapinn@wincor-nixdorf.com (SÃ¶nke Kannapinn) (2000-12-08) |

Re: Meaning of symbol in set theory? eil@kingston.net (John H. Lindsay) (2000-12-08) |

From: | "John H. Lindsay" <eil@kingston.net> |

Newsgroups: | comp.compilers |

Date: | 8 Dec 2000 22:24:00 -0500 |

Organization: | Posted via Supernews, http://www.supernews.com |

References: | 00-12-018 |

Keywords: | theory |

Posted-Date: | 08 Dec 2000 22:24:00 EST |

M Sweger wrote:

.....

*> My question is what is the meaning of the symbol of the backwards*

*> capital E that is sometimes in bold. .....*

The 'backwards capital E' means (a) there is a ...., or (b) there

exists at least one .... . Note also the upside down capital A,

which means for all .... (although some writers express this with

just a pair of parentheses, e.g. (x)(P(x)) which is then read, for

all x for which P(x) is true).

*> Also in the above mentioned paper it talks about "Biconnectivity",*

*> "Strong Connectivity" and "Triconectivity" along with "fronds" and*

*> "cross-links". Have these concept ever been applied to Compilers and*

*> such? My compiler books mention DFS but don't address the*

*> connectivity issues.*

Better dig back through the referenced previous works here; these

graph-theory terms get some strange takes applied to them by particular

writers or writers working in a particular areas.

*> While I'm asking, do any papers for compilers try to apply Group*

*> Theory besides just Graph and Set Theory? .....*

Dunno, never saw any.

*> ..... The only paper I came*

*> across by Tarjan mentioned semigroups. I'll have to dig out a book on*

*> this to find the meaning of this term or go to the mathematical web*

*> page on its definition.*

Semigroup: A set with one associative composition. The

existence of an identity element and invertability are not

assumed; if they were you'd have a group. There are

abelian or commutative semigroups. It's a big subject, and

harder to strangle theorems out of simce less is assumed.

It's useful in handling mathematical operators among many

other things. Only about half of the undergraduate Algebra

texts seem to deal with semigroups at all.

--

John H. Lindsay eil@kingston.net

48 Fairway Hill Crescent, Kingston, Ontario, Canada, K7M 2B4.

Phone: (613) 546-6988 Fax: (613) 542-6987

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