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Paper:

TR03-024 | 25th February 2003 00:00

Weak Cardinality Theorems for First-Order Logic

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TR03-024
Authors: Till Tantau
Publication: 15th April 2003 19:13
Downloads: 1767
Keywords: 


Abstract:

Kummer's cardinality theorem states that a language is recursive
if a Turing machine can exclude for any n words one of the
n + 1 possibilities for the number of words in the language. It
is known that this theorem does not hold for polynomial-time
computations, but there is evidence that it holds for finite
automata: at least weak cardinality theorems hold for finite
automata. This paper shows that some of the recursion-theoretic
and automata-theoretic weak cardinality theorems are
instantiations of purely logical theorems. Apart from unifying
previous results in a single framework, the logical approach
allows us to prove new theorems for other computational models.
For example, weak cardinality theorems hold for Presburger
arithmetic.



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