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- W2267637551 abstract "In this thesis we study inductive definitions over finite structures, particularly, the depth of inductive definitions. We also study infinitary finite variable logic which contains fixed-point logic and we introduce a new complexity measure $textrm{FO}_{bigvee}[f(n),g(n)]$ which counts the number, $f(n)$, of $vee$-symbols, and the number, $g(n)$, of variables, in first-order formulas needed to express a given property. We prove that for $f(n)geq log{n}$, $textrm{NSPACE}[f(n)] subseteq textrm{FO}_{bigvee}[f(n)+left(frac{f(n)}{log{n}}right)^2,frac{f(n)}{log{n}}]$, and that for any $f(n),g(n)$, $textrm{FO}_{bigvee}[f(n),g(n)]subseteq textrm{DSPACE}[f(n)g(n)log{n}]$. Also we study the expressive power of quantifier rank and number of variables and we prove that there is a property of words expressible with two variables and quantifier rank $2^n+2$ but not expressible with quantifier rank $n$ with any number of variables." @default.
- W2267637551 created "2016-06-24" @default.
- W2267637551 creator A5076227056 @default.
- W2267637551 date "2015-08-26" @default.
- W2267637551 modified "2023-09-27" @default.
- W2267637551 title "The Power of the Depth of Iteration in Defining Relations by Induction" @default.
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