Approximate comparison of functions computed by distance automata

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Colcombet, Thomas and Daviaud, Laure (2016) Approximate comparison of functions computed by distance automata. Theory of Computing Systems, 58 (4). pp. 579-613. ISSN 1432-4350

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Abstract

Distance automata are automata weighted over the semiring (Formula presented.) (the tropical semiring). Such automata compute functions from words to (Formula presented.). It is known from Krob that the problems of deciding ‘ f≤g’ or ‘ f=g’ for f and g computed by distance automata is an undecidable problem. The main contribution of this paper is to show that an approximation of this problem is decidable. We present an algorithm which, given ε>0 and two functions f,g computed by distance automata, answers “yes” if f≤(1−ε)g, “no” if f≦̸g, and may answer “yes” or “no” in all other cases. The core argument behind this quasi-decision procedure is an algorithm which is able to provide an approximated finite presentation of the closure under products of sets of matrices over the tropical semiring. Lastly, our theorem of affine domination gives better bounds on the precision of known decision procedures for cost automata, when restricted to distance automata.

Item Type:	Article
Additional Information:	Funding Information: The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n 259454, and from the project ANR 2010 BLAN 0202 02 FREC.
Uncontrolled Keywords:	asymptotic behaviour,comparison,distance automata,tropical semiring,weighted automata,theoretical computer science,computational theory and mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2614
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR) Faculty of Science > Research Groups > Data Science and AI
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	07 Jun 2023 13:30
Last Modified:	10 Dec 2024 01:42
URI:	https://ueaeprints.uea.ac.uk/id/eprint/92314
DOI:	10.1007/s00224-015-9643-3

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