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Automata and logics over finitely varying functions

Chevalier, Fabrice and D'Souza, Deepak and Mohan, M Raj and Prabhakar, Pavithra (2009) Automata and logics over finitely varying functions. In: International Symposium on Logical Foundations of Computer Science (LFCS 2007), JUN 04-07, CUNY, New York, pp. 324-336.

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We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

Item Type: Conference Paper
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Signal languages;First-order logic;Monadic second-order logic;Finite variability.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 18 Jan 2010 06:46
Last Modified: 19 Sep 2010 05:53
URI: http://eprints.iisc.ac.in/id/eprint/25178

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