Tradeoffs between reliability and conciseness of deterministic finite automata

Authors:
Martin Kappes;Chandra M. R. Kintala
Affiliations:
Avaya Labs, Basking Ridge, NJ;Department of Electrical and Computer Engineering, Stevens Institute of Technology, Burchard, Castle Point on Hudson, Hoboken, NJ and Avaya Labs, Basking Ridge, NJ
Venue:
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the fourth international workshop on descriptional complexity of formal systems
Year:
2004

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Abstract

In this paper, we propose a model for measuring the reliability of the description of a language L by a deterministic finite automaton M. Intuitively, the reliability M exhibits when used for L is high if the 'difference' between L and the language T(M) accepted by M is small. Using this model, we prove that the savings in the number of states between a fully reliable and a less reliable representation cannot be bounded by any function, even if the unreliable descriptions are required to exceed any given fixed level of reliability. Furthermore, we show that, for a single regular language, there is a level of reliability such that any description exceeding this level is at least as big as the smallest DFA for the language.