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Abstract: We investigate the expressive power of various extensions of first-order, inductive, and infinitary logic with counting quantifiers. We consider in particular a LOGSPACE extension of first-order logic, and a PTIME extension of fixpoint logic with counters. Counting is a fundamental tool of algorithms. It is essential in the case of unordered structures. Our aim is to understand the expressive power gained with a limited counting ability. We consider two problems: (i) unnested counters, and (ii) ... (Update)
Context of citations to this paper: More
.... theory has been to model the impact of counting on a database language by studying extensions of first order logic by counting quantifiers [16] [10] The goal is to characterize the expressive power of various counting languages, and to identify those with and without good...
...study logics that extend first order with a counting mechanism. Typically, this is done by adding counting quantifiers or terms [8, 11, 14, 20, 29]. Several extensions of FO capture familiar complexity classes over finite structures, and most of the capture results assume that...
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BibTeX entry: (Update)
S. Grumbach and C. Tollu. On the expressive power of counting. Fourth International Conference on Database Theory. 1992. http://citeseer.ist.psu.edu/grumbach94expressive.html More
@article{ grumbach95expressive,
author = "St{\'e}phane Grumbach and Christophe Tollu",
title = "On the expressive power of counting",
journal = "Theoretical Computer Science",
volume = "149",
number = "1",
pages = "67--99",
year = "1995",
url = "citeseer.ist.psu.edu/grumbach94expressive.html" }
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