Linear Circuits Two Variable Logic and Weakly Blocked Monoids 1st Edition by Christoph Behle, Andreas Krebs, Mark Mercer ISBN 9783540744566

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ISBN 10: 
ISBN 13: 9783540744566
Author: Christoph Behle, Andreas Krebs, Mark Mercer

Following recent works connecting two-variable logic to circuits and monoids, we establish, for numerical predicate sets  satisfying a certain closure property, a one-to-one correspondence between <span id="MathJax-Element-1-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="FO[<,ensuremathP]”>��[<,ensuremath�]-uniform linear circuits, two-variable formulae with <span id="MathJax-Element-2-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="ensuremathP”>ensuremath� predicates, and weak block products of monoids. In particular, we consider the case of linear TC⁰, majority quantifiers, and finitely typed monoids. This correspondence will hold for any numerical predicate set which is FO[ < ]-closed and whose predicates do not depend on the input length.

Linear Circuits, Two-Variable Logic and Weakly Blocked Monoids 1st Table of contents:

1 Introduction
2 Definitions
3 Finitely Typed Groups
4 Results
5 Circuits to Logic
6 Logic to Algebra
7 Algebra to Circuit
8 Discus

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