On Complexity of Ehrenfeucht-Fraïssé Games 1st Edition by Bakhadyr Khoussainov, Jiamou Liu – Ebook PDF Instant Download/Delivery. 9783540727347
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ISBN 13: 9783540727347
Author: Bakhadyr Khoussainov, Jiamou Liu
In this paper we initiate the study of Ehrenfeucht-Fraïssé games for some standard finite structures. Examples of such standard structures are equivalence relations, trees, unary relation structures, Boolean algebras, and some of their natural expansions. The paper concerns the following question that we call Ehrenfeucht-Fraïssé problem. Given n ∈ ω as a parameter, two relational structures <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="A”>A and B from one of the classes of structures mentioned above, how efficient is it to decide if Duplicator wins the n-round EF game <span id="MathJax-Element-3-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="Gn(A,B)”>��(�,�)? We provide algorithms for solving the Ehrenfeucht-Fraïssé problem for the mentioned classes of structures. The running times of all the algorithms are bounded by constants. We obtain the values of these constants as functions of n.
On Complexity of Ehrenfeucht-Fraïssé Games 1st Table of contents:
- Ehrenfeucht-Fraïssé Games: Basics
- Complexity of Ehrenfeucht-Fraïssé Games
- Algorithmic Approaches
- Ehrenfeucht-Fraïssé Games and Logic
- Applications and Implications
- Open Problems and Challenges
- Future Directions
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