Download PDF by Su Gao, Steve Jackson, Yi Zhang: Advances in Logic: The North Texas Logic Conference, October

By Su Gao, Steve Jackson, Yi Zhang

ISBN-10: 0486432785

ISBN-13: 9780486432786

ISBN-10: 0821838199

ISBN-13: 9780821838198

ISBN-10: 1719668388

ISBN-13: 9781719668385

ISBN-10: 5319911351

ISBN-13: 9785319911353

ISBN-10: 5519922853

ISBN-13: 9785519922852

ISBN-10: 6720045113

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The articles during this booklet are in accordance with talks given on the North Texas good judgment convention in October of 2004. the most aim of the editors used to be to gather articles representing varied fields inside of good judgment that may either include major new effects and be obtainable to readers with a common historical past in common sense. integrated within the ebook is an issue record, together compiled through the audio system, that displays one of the most vital questions in numerous parts of good judgment. This e-book might be priceless to graduate scholars and researchers alike around the spectrum of mathematical good judgment

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Additional info for Advances in Logic: The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton, Texas

Example text

The problem REACH mentioned above is complete via qfps for the complexity class NSPACE[log n] = NL. Let REACHd be the subset of REACH containing graphs of out-degree at most one. (See Fig. ) REACHd is complete via qfps for Experimental Descriptive Complexity 29 DSPACE[log n] = L. The following containments are well known and easy to prove: L ⊆ NL ⊆ P ⊆ NP . Everyone knows that is is open whether P = NP, but in fact it is open whether L = NP. Since three-colorability of graphs (3-COLOR) is complete for NP via logspace reductions (in fact, fops), it follows that 3-COLOR is reducible to REACHd via qfps iff L= NP.

Consider an algebra A that has no generating set of size 1, that is, where every generating set has size greater than or equal to 2. Let us examine how the translation acts on a Π2n formula of the form ∀y1 ∃x1 . . ∀yn ∃xn φ. The translation works from the inside out; first, the subformula ∀yn ∃xn φ is converted to a constraint formula φ1 . The resulting constraint formula arises as a conjunction (of copies of φ) over a generating set for A, and so by assumption has size at least 2. Then, the translation converts the formula ∀yn−1 ∃xn−1 φ1 to a constraint formula φ2 ; again, the result is a conjunction of copies of φ1 over a generating set for A, and so has size at least 4.

In Descriptive Complexity, our diagrams are generally graphs depicting parts of logical structures before and after queries, or gadgets like the CFI construction. There are many high-quality open-source tools for drawing and labeling graphs. We have implemented a script that transforms the saved output of DE structures into files for GraphViz8 . To make the process as easy as possible, we have added a “draw” command to DE, so that users can make changes to defined structures and then immediately observe their effect.

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Advances in Logic: The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton, Texas by Su Gao, Steve Jackson, Yi Zhang

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